Cristiano Ronaldo scored his first ever goal at Anfield to give Real Madrid the perfect start against Liverpool.
Karim Benzema made it 2-0 with a fine looping header as Real took control.
Benzema's second right before the break gave Real a 3-0 advantage as Liverpool capitulated.
Liverpool's Raheem Sterling endured a frustrating night as his side failed to find a way back into the contest.
Antoine Griezmann was on target as Spanish champion Atletico Madrid defeated Malmo 5-0 at Vicente Calderon.
Borussia Dortmund put its domestic worries aside to claim a third consecutive Champions League victory following a 3-0 win over Galatasaray.
Rampant Ronaldo
Heading to victory
Real deal
No way through
Goal for Griezmann
Dortmund delight
STORY HIGHLIGHTS
- Real Madrid thrashes Liverpool 3-0 in Champions League
- Cristiano Ronaldo opened scoring
- Karim Benzema grabbed two
- Juventus stunned by Olympiakos
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(CNN) -- Booed and jeered upon his entrance, cheered upon his exit -- perhaps even the most bitter of rivals are finally ready to submit to the mercurial talents of Cristiano Ronaldo.
Few former Manchester United players have been given the ovation which Ronaldo received from an Anfield crowd, but then again, this is not just any player.
Ronaldo had never scored at Anfield during his time with United -- it was a statistic which took just 23 minutes to become history.
A 3-0 victory over Liverpool, inspired by Ronaldo, ensured Real Madrid made it nine points out of nine in Group B.
A 70th Champions League strike means he is just one behind the all-time leading scorer, Raul, the man so revered by all at Real.
The record will soon fall, Ronaldo and Lionel Messi, who has 69, will set records which few would have ever imagined possible.
For Real, a club record seventh consecutive European victory was assured courtesy of Ronaldo's breathtaking strike and Karim Benzema's double.
For all the pre-match hype of another 'special European night' at Anfield, it was all pretty routine.
Liverpool, the five-time winner, was blown away by the pace and power of Real as Ronaldo took center stage.
"It was special, my first goal at Anfield and I am very happy -- amazing," Ronaldo told Sky Sports
"We knew that Anfield is a difficult place, but we were fantastic in the first 45 minutes and we deserved to win.
"I'm not worried about the Champions League goalscoring record. I know I will beat it. Me and Lionel Messi are very close.
"The best thing is that the team has nine points.
"Can we retain the cup? Why not? We are taking it step-by-step but we are going to try.
"We know it will be tough but we are positive and it is possible."
No team has ever managed to retain the Champions League title since it was revamped into its current format in 1992, but Real will certainly go close in it attempt to record an unprecedented 11th triumph.
A day after Bayern Munich had ransacked Rome by scoring seven, Real arrived at another of European football's most famous fortresses and blew it to smithereens.
Roma rout
Brilliant Bayern
Shakhtar's six-shooters
Messi on the brink
Aguero strike
Sting in the tail
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Bayern cut loose in Roma
Weekend football action
Weekend football action
Weekend football action
Weekend football action
Weekend football action
Weekend football action
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Goals galore in European leagues

"It's Rome," jokes James Pallotta, the president of AS Roma, explaining his decision to invest in the Italian football club.
American Pallotta has some ambitious plans for the Italian football club.
Pallotta wants to capitalise on Rome's historic past, but the Bostonian also has a vision for the future, notably building a new stadium for the Serie A team.
The new Roma Stadium is set to open in time for the 2016/17 season. The club will move away from the Stadio Olimpico which was opened in 1953.
The capacity at the new stadium will be 52,000 but can be enlarged to 60,000 if required. It will have parking for 7,000 cars and will be supported by the local metro station.
The stadium will be flanked by a new training center which will be used by the first team as well as the youth players.
Fans will be able to visit Roma village where there will be a number of bars, shops and restaurants before making their way to the stadium.
The new 'Curva Sud' will house the team's hardcore fans has space for 13,660 supporters.
Francesco Totti is a Roma legend and the 38-year-old has spent his entire career with the club.
Totti made his debut for Roma at the age of 16 and is still a key member of Rudi Garcia's team.
Garcia is forging a reputation as one of the most impressive coaches in European football. Since joining from French club Lille in June 2013, Garcia has helped take Roma to the next level with a series of encouraging displays.
Roma striker Gervinho (left) celebrates with teammate Miralem Pjanic. Both players have blossomed under Garcia's tutelage.
A new Roman Empire?
A new Roman Empire?
A new Roman Empire?
A new Roman Empire?
A new Roman Empire?
A new Roman Empire?
A new Roman Empire?
A new Roman Empire?
A new Roman Empire?
A new Roman Empire?
A new Roman Empire?
A new Roman Empire?
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A new Roman Empire?
This was a result that most would have anticipated given Liverpool's stuttering start to the season but the way in which Real scythed through its opponents was nothing short of exquisite.
Deprived of Gareth Bale, who remained in the Spanish capital nursing an injury, Real was able to call on its hosts of stars as it taught Liverpool a lesson in the art of attacking football.
In James Rodriguez, Toni Kroos, Luka Modric and Isco, Real boasted a midfield which most teams could only dream of.
While Liverpool, so inconsistent following the success of last season and the departure of Luis Suarez, has struggled in recent weeks, Real has been on cruise control.
Seven consecutive victories which have yielded 32 goals meant Real arrived as favorites at a stadium where it had never managed to win before.
And yet, any doubts over its ability to break its three-game losing streak against Liverpool were soon extinguished.
The breakthrough came after 23 minutes -- and it was worth waiting for.
Ronaldo, who appeared to induce panic each and every time he as much as breathed, laid the ball off to James Rodriguez, who in turn produced a quite sumptuous pass over the top of the Liverpool defense.
With those in red caught watching the flight of the ball, Ronaldo ran in behind and produced a finish which belied belief, flicking the ball into the far corner with unerring accuracy.
That strike, the forward's 20th in 13 games this season, seemed to leave Liverpool winded -- a blow from which it never recovered.
Seven minutes later, the contest was all but over as Benzema pulled away at the far post to send a looping header into the opposite corner following rather questionable Liverpool defending.
In the three previous meetings between the two sides, Real had never managed a goal, let alone a victory.
Defeated 4-0 on its last visit to Anfield five years ago, Real appeared determined to exorcize its demons.
A third goal followed just before the interval, Benzema once again the grateful recipient of some more woeful home defending.
To its credit, Liverpool refused to give up after falling three goals behind and only the post denied Philippe Coutinho from dragging his side back into the contest.
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The second half was a rather tame affair as Liverpool briefly attempted to launch a response, though without the disappointing Mario Balotelli, who was withdrawn at the interval.
With the first Clasico of the season on Saturday, Real took its foot off the gas, though more goals should have been forthcoming.
Ronaldo should have added a fourth midway through the second half after the visiting side had cut through the Liverpool defense with embarrassing ease, but for once, the Portuguese forward was unable to find a way past goalkeeper Simon Mignolet.
In the end, Ronaldo had to settle for a solitary strike and an early exit as he was replaced with 15 minutes remaining as Carlo Ancelotti, the Real Madrid coach, began to look towards Saturday's clash with Barcelona.
"It was the best we have played all season," said Ancelotti.
"We were fantastic in the first half and then controlled the game. I had to say nothing to the players, they played really well.
"I am lucky to manage this group of players."
Liverpool will face Real once more in a fortnight's time in the return game but it's chances of qualification remain in the balance.
"The first 22 minutes of the game we were excellent but from the first goal to halftime, Real Madrid showed their real quality," Brendan Rodgers, the Liverpool manager, told Sky Sports.
"They were terrific. Second half we played for pride and we were outstanding, the players kept going, they didn't stop. We defended poorly but I can't ask any more.

Leading Italian club Internazionale last won a trophy in 2011. Can Indonesian businessman Erick Thohir restore Inter to its former glories?
The 44-year-old Thohir took a 70% stake in Inter just under a year ago. He is one of only two foreign owners in Serie A.
Thohir, who is also a part owner of American MLS club DC United, says it is a "dream come true, an unbelievable story to own Inter, I never imagined it."
Serbian defender Nemanja Vidic joined Inter in preseason, but had an inauspicious start after being sent off in his first league game against Torino.
Inter coach Walter Mazzarri was already in charge when Thohir took over the club, and with the team having lost its previous two league games he is under pressure to secure a win against Napoli on Sunday.
Inter shares the San Siro stadium with AC Milan, but the Nerazzurri rarely fill the venue's 80,000 capacity for home games.
Thohir is a great believer in the power of globalization. Inter toured the United States in preseason and 62,000 fans watched this friendly against Real Madrid in Berkeley, California.
Inter's chief executive officer is Michael Bolingbroke, who previously worked for Manchester United, and is pictured sitting next to Inter vice-president Javier Zanetti.
Zanetti retired at the end of last season after 19 years playing for the club. An Inter fan is pictured wiping away a tear after the 40-year-old Argentine said farewell to supporters following a 4-1 win over Lazio at the San Siro in May.
In 2010, Inter's then coach Jose Mourinho -- now at Chelsea -- guided the Serie A team to an unprecedented treble: the Italian league and cup as well as the European Champions League, beating Bayern Munich in Madrid.
Former president Massimo Moratti stayed on as a member of the board after Thohir's arrival.
During the Moratti era, Inter splashed out in the transfer market, notably buying Brazilian striker Ronaldo from Barcelona in 1997 for $27.9 million.
The hardcore supporters of Italian football provide the pageantry for Serie A, but are they ready to embrace Thohir's message?
AS Roma's American president James Pallotta (L) is Serie A's other foreign owner.
Serie A champion Juventus is the only team in Italy's top division to own its ground. The Juventus Stadium was opened in 2011 and holds 41,000 spectators.
Inter-regnum
New kid on the block
Dream opportunity
Veni vidi Vidic
Under pressure
Shared tenants
Embracing globalization
New boardroom broom
Inter Milan's new owner Erick Thohir
Mourinho era
Moratti legacy
Spend, spend, spend
Ultra concerns?
Roman rivals
Old Lady, new home
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Inter Milan's new owner Erick Thohir

He wears the number 10 on his back and he's spent the past decade delighting football fans across the world. Lionel Messi's achievements for Barcelona have led to many branding the Argentine the greatest player of all time. After 10 years of golden glory, it's easy to see how Messi has taken his place among the football gods.
Messi's debut came against Espanyol on October 16, 2004. The 17-year-old came on as a substitute, replacing Portuguese midfielder Deco. The teen sensation would have to wait seven months for his first Barca goal, which came against Albacete on May 1, 2005.
Hot on the heels of his first senior goal, Messi made his debut for the Argentine national side in a friendly against Hungary on August 17.
Messi's reputation continued to grow and he showed his devastating potential on March 11, 2007. Matches between Barca and its archrival Real Madrid are dubbed "El Clasico" and regarded as one of the biggest games in the sport. Messi showed he belonged on the highest level with a hat-trick as the two teams drew 3-3.
Barca lifted the European Champions League trophy in 2009, with Messi scoring the second goal in a 2-0 win over Manchester United in Rome. The club completed a treble of Spanish league, cup and European Cup triumphs in an historic season.
Messi's contribution to Barca's success was recognized as he was awarded the Ballon d'Or, the prize annually awarded to the world's best player. He has gone on to lift the gong on three further occasions.
By May 2011, he had fired Barca into another Champions League final, once again against Man Utd at Wembley. Messi scored as Barca outclassed the English champions, securing a comfortable 3-1 win and third European Cup triumph in six years. Predictably, Messi was awarded a third straight Ballon d'Or in December 2011.
A moment of destiny arrived for Messi on March 2012 during a match against Granada. He bagged a hat-trick to move on to 235 goals for Barca and overtake Cesar Rodriguez as the club's all-time leading goalscorer. Cesar played for Barca between 1939 and 1955.
Messi's goalscoring exploits scaled new heights in 2012. A strike against Valladolid on December 22 was his 91st of the calendar year, breaking a record previously held by Germany's Gerd Muller.
Barca reigned in Spain during the 2012-13 season, running away with the league title by racking up 100 points. During his 10 years at the Nou Camp, Messi has won six league titles and two Spanish Cups in addition to three Champions League crowns.
Messi led Argentina at the 2014 World Cup in Brazil earlier this year. As captain, he scored four as the South Americans advanced to a final meeting with Germany. However, even Messi couldn't guide Argentina to football's greatest prize, as Mario Gotze scored in extra-time to seal a win for the Germans.
Lionel Messi: A decade of goals
Lionel Messi: A decade of goals
Lionel Messi: A decade of goals
Lionel Messi: A decade of goals
Lionel Messi: A decade of goals
Lionel Messi: A decade of goals
Lionel Messi: A decade of goals
Lionel Messi: A decade of goals
Lionel Messi: A decade of goals
Lionel Messi: A decade of goals
Lionel Messi: A decade of goals
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Lionel Messi: A decade of goals

Mario Balotelli has had a low key start to his Liverpool career after a big-money move from Italian giants AC Milan. The English club finished runner-up in the Premier League last season but have stuttered so far, losing six of its 13 competitive fixtures.
Balotelli has failed to scored a goal in those 13 matches for his new club after a move reported to be worth $25 million. "We got to a point when we were looking for a different kind of player and he was looking for a different challenge," Milan director Umberto Gandini told CNN of Balotelli's departure from Milan.
Balotelli has also shown flashes of the temper that have punctuated his career since returning to England -- confronting West Ham United goalkeeper Adrian during Liverpool's 3-1 defeat in September.
Balotelli's first stint in England came with current Premier League champions Manchester City between August 2010 and January 2013. Perhaps his defining moment in sky blue came when he scored during City's 6-1 derby demolition of Manchester United and revealed a t-shirt that read "Why always me?"
Balotelli has 33 caps for Italy, scoring 13 goals, the last being his winner in the 2014 World Cup group stage clash against England. But that be would the Azzurri's only success in Brazil, as they suffered a shock 1-0 defeat to Costa Rica before another one goal defeat -- to Uruguay -- eliminated them.
After the World Cup, Balotelli failed to make two Italy squads, perhaps reflecting his indifferent form for Liverpool, though he was recalled in November, before picking an injury on international duty.
Balotelli burst onto the scene with AC Milan's city neighbors Internazionale in December 2007. He had a fractious relationship with then Inter boss Jose Mourinho, leaving for Manchester City in 2010 after scoring 20 goals in 59 matches for the club.
Balotelli's move from City to AC Milan angered Inter fans, who share a stadium with its city rivals. Gandini hailed Balotelli's contribution in his first season at the club as his goal helped it make the European Champions League.
But after just one full campaign with the club Balotelli was on the move for the fourth time in his fledgling career, his new manager Brendan Rodgers admitting signing the striker was a "calculated risk," given his disciplinary problems and off-field antics.
Gandini said of the mercurial player: "The expectation was probably bigger (at AC Milan), and I think also his expectations, and he has not reached the status yet where he can carry the club. Until he will do that he won't be able to fulfill his promises. I hope he does fulfill his potential, for him, for Liverpool and for the national team."
Super Mario?
Goal shy
Red mist
City slicker
Proud Italian
Out in the cold
Young gun
Milan's main man
On the move
Last chance saloon?
HIDE CAPTION
Super Mario's last chance?
"You can see Real's quality. Speed, technique; you can see why they are champions.
"The second and third goals are from set-pieces again, it's an issue for us and we have to be better than that."
The defeat leaves Liverpool on three points, level with Bulgarian side Ludogorets and Swiss club Basel.
Ludogorets claimed its first ever Champions League victory with a 1-0 win over Basel.
Juventus beaten
Elsewhere, Juventus suffered a shock 1-0 defeat away at Olympiakos.
The Italian side, top of Serie A, was beaten by a Pajtim Kasami strike as the Greeks made it two home wins out of two.
Atletico Madrid, which was beaten on its visit to Greece, eased to a 5-0 victory over Swedish club Malmo.
Atletico, beaten in last season's final, scored all five goals in the second half.
In Group D, Borussia Dortmund made it three wins out of three with an emphatic 4-0 thrashing of Galatasaray.
Arsenal sits second after scoring twice in the final two minutes to steal a 2-1 win at Anderlecht.
In Group C, Bayer Leverkusen overcame Zenit St Petersburg 2-0, while Monaco and Benfica finished goalless.
Read: Where is Mario Balotelli?
Read: Cristiano Ronaldo's Facebook fan club