Barcelona are now four points adrift of leaders Real Madrid after a 0-0 draw at Getafe on Saturday.
Real Madrid sealed their 20th victory in a row in all competitions and are now only four off the world record set by the Brazilian side Coritiba in 2011.
Not to be outdone, Lionel Messi also bagged a hat-trick as Barcelona eased past city rivals Espanyol 5-1 on Sunday, Pique and Pedro scoring one each and Garcia de la Fuente grabbing a goal for the visitors.
Cristiano Ronaldo scored his 23rd hat-trick – a new record – as Real Madrid beat Celta de Vigo 3-0 to record their 18th straight win, a new club record.
Barcelona snatched victory at the very last moment against Valencia, Sergio Busquets slamming the ball home in the 94th minute.
Ñiguez and Turan scored as Atlético Madrid beat Deportivo La Coruña 2-0 to move, at least temporarily, into second place in La Liga pending the result of the Valencia-Barcelona match.
Sixteen wins in a row now, a new club record, for Real Madrid, after a 1-2 win at Málaga.
Valencia could have moved up into third place in La Liga, had they not lost 2-1 at Levante.
Málaga couldn’t keep their recent run of good form going as they lost 3-1 to Atlético Madrid.
Atlético Madrid got off to a good start against struggling Real Sociedad after Mandzukic netted after ten minutes, but the party didn’t last as Vela equalised just five minutes later.