With Barcelona suffering a shock home defeat by Malaga on Saturday, Real had a chance to go four points clear and they grabbed it with second-half goals by Karim Benzema and Ronaldo.
Although the Portugal forward struck a curling shot against the post after four minutes, Real struggled to break down a team that worked hard and were guilty of some aggressive challenges.
Benzema was unlucky to have a spectacular overhead kick ruled out due to a questionable offside call but he did knock a loose ball in from close range after 56 minutes.
Ronaldo then sealed the victory with a powerful header into the top corner from an Isco cross after 70 minutes.
It was a welcome goal for Ronaldo who has suffered a dip in form since Christmas following an electrifying start to the season and has now moved joint third in Real's all-time list.
The Portuguese now has 290 goals and is level with Carlos Santillana, while Raul is out in front on 323.
“We're trying to rediscover our best form and we know that in a short amount of time everything can change,” Real goalkeeper Iker Casillas, who celebrated his 500th La Liga match, told reporters.
“We received a lot of criticism but now the situation is more relaxed but this situation is normal playing for Real Madrid.
“Our attitude has always been right and it is usual that you have ups and downs in form. When you are down it is when you have to be more united and that has been the case.
LATE WINNER
Earlier Real Sociedad came out on top in a 4-3 thriller against Sevilla when Xabi Prieto headed a late winner.
A Luciano Vietto goal after 71 minutes gave Villarreal a 1-0 home win over Eibar and Athletic Bilbao beat visiting Rayo Vallecano 1-0 with a late Aritz Aduriz strike.
Real once again started by deploying Lucas Silva in midfield with James Rodriguez and Sami Khedira injured and Asier Illarramendi still out of favour with coach Carlos Ancelotti.
Ronaldo was unfortunate with his early strike from the left of the area that hit the woodwork but he then fluffed a shot with the goal gaping after being found by Gareth Bale.
The visitors pushed forward and the Elche rearguard resorted to some combative tackles to keep them at bay.
Full back Eduardo Albacar was booked midway through the first half after several fouls on Bale on the wing. Then early in the second half Aaron Niguez should have been dismissed for a reckless two-footed lunge on the Welshman.
While Benzema’s acrobatic effort was ruled out in the first half he scored with a more mundane goal when he tapped in after a David Lomban clearance rebounded off keeper Przemyslaw Tyton and fell to the France striker.
Ronaldo started the game with a return of just three goals from six league games since Christmas and, although still not at his best, showed his usual desire and was rewarded with Real’s second goal of the night.
The win put some daylight between Real and Barca, whose 11-match winning run came to an end with a surprise 1-0 defeat by Malaga at the Nou Camp, at the top of the table.
(Editing by Ken Ferris)
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