Centre-back Pepe headed home the match winner from Luka Modric's 55th-minute free-kick as Madrid took full advantage of the goalless draw between joint pacesetters Barcelona and Atletico Madrid on Saturday night.
The victory was Madrid's eighth in nine games since their last league loss, which was the 2-1 defeat at Barca in October, but it was closer than they would have liked after they failed to make the most of a host of chances to finish the game off.
For once, it was Cristiano Ronaldo - who brought up 400 career goals in Madrid's win over Celta Vigo last week and who could win the FIFA Ballon d'Or award on Monday - who had forgotten his shooting boots as he missed out on a hat-trick of great openings in the final half-hour.
At the other end of the Primera Division standings, Real Betis fell five points adrift of their rivals in the relegation zone after they lost 2-1 at home to Osasuna while second-bottom Rayo Vallecano won 1-0 at Getafe.
Little went Betis' way as they slumped to a 12th defeat of the season, going behind after just two minutes to a Roberto Torres goal, being reduced to 10 men before the break when Nono was sent off and then seeing Osasuna double their lead with a 57-minute own goal from Jordi Figueras.
Betis looked to have been handed a lifeline when Osasuna goalkeeper Andres Fernandez was sent off in conceding a penalty on the hour-mark, but the home side could not even capitalise on that gift as Ruben Castro smashed his spot-kick against the crossbar.
Betis did finally manage to pull a goal back through substitute Jorge Molina 10 minutes from time, but it was too little too late to save them.
To make matters worse for the Seville-based outfit, their nearest rivals at the foot of the standings Rayo had picked up a valuable three-point haul earlier in the day.
Alberto Bueno notched the only goal of the game on 29 minutes as Rayo earned just fifth win of the season while Madrid neighbours Getafe crashed to a fourth successive defeat.
In the day's other game, Levante picked up a much-needed victory over Malaga. The Valencia-based side, who had lost six of their previous seven league games, leap-frogged Malaga and up to 10th with a 1-0 victory thanks to David Barral's 19th-minute goal.