The Portuguese winger and Karim Benzema struck in the second half to ensure that Carlo Ancelotti's men set 2014 off on winning ways at the Bernabeu.Cristiano Ronaldo helped Real Madrid kick off the new year with a 3-0 win at home to Celta.
Leading duo Barcelona and Atletico Madrid began 2014 with wins at the weekend and, while the Blancos were not at their fluent best, they kept within five points of both ahead of the champions' trip to the Vicente Calderon on Saturday.
Following a fairly even opening hour, Karim Benzema was on hand to register the opener, applying a finish to substitute Jese's cross after 67 minutes to settle Real's nerves, before Ronaldo's late double wrapped up the points.
Carlo Ancelotti recalled defender Pepe to his starting XI following a suspension, while Gareth Bale was named on the bench after he missed the trip to Valencia prior to the mid-season break with a calf injury.
Celta had won just once in its last five league matches going into the game, and former Madrid midfielder Luis Enrique opted for a change up front as Charles replaced Santi Mina.
Despite their poor form, the visitors should have taken the lead after five minutes when Charles' effort found the side netting when clean through on goal.
The hosts quickly began to dominate possession but struggled to fashion chances until Luka Modric fizzed a long-range effort just over Yoel's crossbar.
Benzema then saw an effort deflected wide from inside the area after 26 minutes as Ancelotti's men were frustrated by a stubborn Celta back line.
The visitors threatened regularly on the counter, however, with Rafinha's shot deflected over the bar by Pepe when he perhaps should have squared it wide to the unmarked Fabian Orellano before the break.
Isco did well to fashion an effort after a superb turn away from Gustavo Cabral but his tame shot was easily saved by Yoel before Jese saw his tame strike easily saved after on the hour.
Bale was introduced to boost the hosts' attacking threat after 64 minutes, but it was Jese who again impressed for Ancelotti's men.
Having scored the winner against Valencia before the winter break, he produced a clever piece of skill in the area before crossing for Benzema to stab home.
Only Barcelona can better Celta's win record as an away side at the Santiago Bernabeu in the last 10 years, but Ronaldo's close-range finish was enough to put any chance of an upset to bed.
Bale then cut the ball back for Ronaldo to register his 20th Liga goal of the season in injury time as Celta, who failed to score away in the top flight for a second game running, dropped into the relegation zone.