Karim Benzema scored the only goal of the game on 40 minutes from a Luka Modric assist as the Blancos really start to stamp their authority on the Spanish title race.
Carlo Ancelotti's men have now won seven games in a row in all competitions and have lost just one of their 14 La Liga matches.
They are seven points ahead of champions Atletico Madrid, although their cross-city rivals do have a game in hand.
Madrid's game against Athletic was the only match of the night in La Liga.
Madrid are back in action against another Basque opponent on Saturday as they travel to play third-placed Real Sociedad. Another win there and they will be in an even stronger title position.
Barcelona host Real Betis, hoping to extend their three-match unbeaten run since Xavi took over as manager. Barca are five points from a Champions League spot, with fourth placed Sevilla hosting Villarreal in another big game.
LA LIGA STATISTICS: