(CNN) -- Russia emerged as genuine contenders for football's European crown with a thumping 4-1 win over Czech Republic after co-hosts Poland and 2004 champions Greece had opened the tournament with a dramatic 1-1 draw in Warsaw.
Alan Dzagoev scored twice as Dick Advocaat's Russia side made a confident start, Roman Shirokov and substitute Roman Pavlyuchenko completing the rout after Jaroslav Plasil had briefly threatened a Czech comeback.
Russia, who reached the semi-finals of Euro 2008 under Guus Hiddink, next face co-hosts Poland, who saw Robert Lewandowski's first-half header cancelled out by Greece substitute Dimitris Salpingidis' second-half goal in Warsaw.
But the goalscorers barely told the tale of a remarkable opening match.
Both sides had a player sent off - Sokratis Papastathopoulos for Greece and Poland goalkeeper Wojciech Szczesny -- before the Arsenal goalkeeper's replacement Przemyslaw Tyton emerged as the hero by saving a penalty from Giorgos Karagounis.
Poland 1-1 Greece
Two goals, two red cards and a missed penalty in the tournament's opening game meant that the focus of Euro 2012 shifted firmly to football.
Fears of racism had dominated the build-up to the tournament and there was an inevitable feeling of relief when the opening game finally got under way in Warsaw.
A brief but beautiful opening ceremony - just 12 minutes long - set the scene for the three-week tournament before the home crowd came close to lifting the closed roof off the National Stadium with a rousing rendition of the national anthem.
It was a vocal chorused outside the stadium by 100,000 supporters crammed into a specially-built fan zone in the center of Warsaw -- and those almost exclusively Poland fans had plenty to shout about in the opening 20 minutes of the opening game.
Co-hosts Poland looked to be cruising to their first-ever European Championship finals victory when Borussia Dortmund striker Lewandowski headed home Jakub Blaszczykowski's cross, with Greece keeper Kostas Chalkias stuck in no-man's land.
It was a special moment for Lewandowski, who was born in Warsaw and proved a constant menace to the hapless Greek defence in a one-sided first half.
And when Greece lost both their starting centre backs - Avraam Papadopoulos limping off injured before Papastathopoulos was sent off for two bookings in nine first-half minutes -- it seemed a matter of how many for Lewandowski and Poland.
Somehow, Greece manager Fernando Santos instigated a response to silence the Polish fans in and out of the stadium, with substitute Salpigidis the central character.
Just six minutes after coming on as a half-time substitute, Salpigidis poked an equaliser past stranded goalkeeper Szczesny.
Suddenly it was the Greek fans - so burdened by national crisis, so weighed down by Eurozone millstones - with something to celebrate.
It got worse for Arsenal keeper Szczesny when he saw red for a clumsy trip on substitute Salpigidis, but his replacement Tyton guessed right to push away Greece captain Karagounis' penalty.
The Warsaw party was back on -- and two of the tournament underdogs had set a high standard of entertainment for the rest to follow.
Russia 4-1 Czech Republic
Over in Wroclaw, Russia and Czech Republic continued to defy Group A's pre-tournament image as the "least exciting" section, with Advocaat's side capitalising on some weak Czech defending.
These two sides had been installed as favourites to qualify from the group, but only the Russians lived up to that hype in a game dominated by Advocaat's side.
Former Arsenal forward Arshavin was the architecht of their dominance, playing a crucial part in the opening goal from Dzagoev and then playing a defence-splitting pass to set up Shirokov for the second.
Pilar's superbly taken goal early in the second half gave the Czechs hope and they had chances to level before substitute Pavlyuchenko set up Dzagoev for his second and then himself wrapped up victory with a thumping finish.
Pavlyuchenko had been ledft out of Russia's starting line-up, yet still played a crucial role in helping finish off the Czechs when he replaced the tiring Aleksandr Kerzhakov 17 minutes from time.
It was a cameo role not lost on two-goal hero Dzagoev, who told Uefa's official website: "It was hard for us at 2-1 but a big performance from Roman helped us and we want to thank him for this.
"It is very important that we performed well in the first game -- it is one of the six steps to the final."
Czech Republic coach Michal Bilek admitted his side had struggled to cope with the Russians' forward movement and link-up play. He conceded: "We had problems with the combinations of the Russians. They had a lot of chances and we could not get the ball off them.
Bilek added: "They have great technique and showed us today what a great team they are."