Pedro, Lionel Messi and Andres Iniesta scored the goals that that earned Barca a 14th consecutive league victory, equalling the previous club record set under Frank Rijkaard when they won a La Liga and Champions League double in the 2005/06 season.
Valencia climbed to third on 40 points after Aritz Aduriz grabbed a last-minute goal to earn his side a thrilling 4-3 comeback win at home to nine-man Malaga.
Earlier, Luis Fabiano's hat-trick fired Sevilla to a 4-1 win over Levante that put them seventh with 29 points.
"Against a rival like Real Madrid nothing is ever decided until the very end," he told reporters. "Tomorrow they will be four points behind us again because they have the best coach in the world and a very good team."
Malaga's new-look side deservedly took the lead at Mestalla when Jose Rondon stroked in an 11th-minute opener, but they were quickly down to 10 men as Martin Demichelis was sent off for tripping Juan Mata in the area.
The Spain winger levelled from the penalty spot, only for Malaga's Rondon to score again from a freekick in the 35th.
In Seville, Brazil striker Luis Fabiano scored with a header, a penalty, and a shot from the edge of the area to boost Sevilla ahead of next week's King's Cup semi-final against Real.
Fabiano guided a majestic header into the top corner from a Jesus Navas cross in the 28th minute, and Julien Escude doubled Sevilla's lead at a corner in the 39th.
