Jese Rodriguez, Karim Benzema and Luka Modric all found the net as Real matched La Liga leaders Barcelona and Atletico Madrid, who both recorded victories on Saturday.
After Jese scored his fifth goal in the last six games, Benzema doubled his side's advantage as Real made it 100 goals for the season.
Modric then added a third six minutes after the hour to leave the top three teams level on 60 points after 24 games.
Fourth-placed Athletic Bilbao fell further away from the top three when they were beaten at home for the first time in the league this season.
Sergio Garcia gave visitors Espanyol the lead six minutes in before Carlos Gurpegui restored parity an hour later.
Diego Colotto struck the winner nine minutes later as Espanyol became the first side to complete the double over Athletic this season, with the hosts' misery compounded late on when Aritz Aduriz was shown a second yellow card.
Piti's expert finish from inside the area 31 minutes in handed Granada a 1-0 victory over rock-bottom Real Betis at the Estadio Nuevo Los Carmenes as the visitors missed the chance to make up any ground on the two other sides in the bottom three.
Betis now sit 10 points off Malaga in 17th, with Bernd Schuster's men hosting Real Sociedad on Monday.
Sunday's final game saw Sevilla and Valencia play out a goalless draw with both sides ending the match with 10 men.
Ivan Rakitic missed a penalty three minutes after the hour mark, shortly after Ricardo Costa had picked up his second yellow card.
Substitute Denis Cheryshev was then shown two yellow cards in his 31-minute appearance to earn himself a red as both sides remain level on points in La Liga.
