Just a few short weeks ago Barcelona had one hand on the trophy with a nine-point lead, but a slump in form and defeat in the El Clasico a fortnight ago has given both Real and Atletico Madrid renewed hope.
Barcelona plays Valencia Sunday in a bid to re-open the four-point gap to its arch rival, while Atletico, which knocked the Catalan giant out the Champions League in midweek, faces lowly Granada.
Karim Benzema and Isco with first half goals put Real in control and after the break more goals flowed.
Gareth Bale made it 3-0 before Pablo Sarabia pulled one back for the home side against his former side.
Late goals from James Rodriguez and finally Cristiano Ronaldo rubbed it in for the visitor.
It was Ronaldo's 47th goal of the season and followed his hat-trick in midweek as Real retrieved a two-goal deficit to beat Wolfsburg in their Champions League quarterfinal tie.
The victory is further evidence of the Los Blancos revival since Zinedine Zidane took over from Rafa Benitez, with a seventh straight La Liga victory, including the 2-1 El Clasico triumph.
A record 11th victory in Europe's premier club competition is a real possibility, particularly with the exit of holder Barcelona, but Zidane is not settling for just that believing La Liga is still within reach.
" Today I wouldn't sign for that," he said. "We need to keep going until the end of the season."
Manchester sides win in EPL
In the English Premier League, Marcus Rashford enhanced his growing reputation with the only goal of the game as Manchester United condemned Aston Villa to its inevitable relegation with a 1-0 win at Old Trafford.
Wayne Rooney, returning from injury, started for United before being substituted in the second half of a routine win for Louis van Gaal's side.
But neighbor Manchester City later beat Chelsea 3-0 at Stamford Bridge to keep a four-point gap to its city rival in the battle for the fourth Champions League spot in England.
It was another fine display from City, which reached the Champions League last four for the first time in its history in midweek, with goals either side of halftime from the prolific Sergio Aguero, both on counter attacks, putting Manuel Pellegrini's men in command.
Aguero, who missed a penalty in City's 1-0 win over Paris St. Germain to reach the last four, then completed his hat-trick from the spot after Chelsea goalkeeper Thibaut Courtois was shown red for pulling down Fernandinho.
Cit moves up to third, one point ahead of Arsenal, which is at home to Crystal Palace Sunday.
In the relegation battle, Newcastle, now managed by Benitez, scored a vital 3-0 win over Swansea to keep alive its slim hopes of survival.
Jamaal Lascelles, Moussa Sissoko and finally in-form Andros Townsend netted for the home side to help Benitez celebrate his 56th birthday in style.
That victory was vital after north-east rival and fellow relegation battler Sunderland earlier won 3-0 at fourth-bottom Norwich.
Goals from Fabio Borino, with a first half penalty, Jermain Defoe, his 13th in the EPL this season, and Duncan Watmore sealed the three points for Sam Allardyce's team.
It has closed to within a point of Norwich with Newcastle a further two points adrift , both having played a game less than the East Anglian side.