Luis Suarez scored the decisive goal in the 54th minute, converting a Sergi Roberto pass from close range after Ivan Rakitic had taken advantage of a huge gap in the Madrid midfield.
Less than 10 minutes later a goalmouth scramble saw Dani Carvajal sent off for handball in the penalty area before Lionel Messi converted the subsequent penalty.
In added time substitute Aleix Vidal added a third to round off the victory with a low strike that crept over the goal line after Keylor Navas failed to hold it.
Ahead of the winter break Valencia can reduce Barca's lead at the top to eight points should they beat Villarreal later in the day.
Madrid, meanwhile, sit back in fourth and 14 points behind the league leaders.