The French striker opened the scoring by netting from close range after a good run down left from his Portuguese team-mate, who then sealed victory with a powerful header
Barcelona's surprise 1-0 home reverse at the hands of Malaga on Saturday gave Real the chance to extend their advantage at the top 24 hours later, and they overcame a profligate first half to seal maximum points.
After seeing an acrobatic effort wrongly ruled out for offside before the break, Karim Benzema struck from close range 11 minutes after the interval for his 18th goal of the season in all competitions.
Cristiano Ronaldo had endured a frustrating first half that saw him hit the woodwork and miss two presentable opportunities, but the Portuguese netted his 38th goal of the campaign with a trademark header midway through the second period.
It was Ronaldo's seventh in just three appearances against Elche, who failed to seriously trouble Iker Casillas - making his 500th La Liga appearance - in the Real goal.
Victory sees Ancelotti's side put further daylight between themselves and the chasing duo of Barca and Atletico Madrid, while defeat for Elche leaves them 17th in the table, four points clear of the bottom three.
Ronaldo, fresh from ending a three-game scoreless run against Schalke in midweek, went close to the opener in the fourth minute when he curled a superb effort against the outside of the post.
The visitors threatened again seven minutes later, but Elche goalkeeper Przemyslaw Tyton was able to smother Gareth Bale's effort from close range.
Tyton had to be alert to save from Ronaldo again soon afterwards as Real continued to dominate, and the Portuguese uncharacteristically made a mess of Bale's square pass when it seemed he would tap home from six yards.
Real ought to have been in front five minutes prior to the interval when Benzema produced a superb overhead finish to convert Bale's centre, but the assistant referee incorrectly ruled the Frenchman to have been offside.
After a first half that saw one-way traffic towards the Elche goal, Casillas was tested for the first time two minutes into the second period when he got down to keep out Aaron Niguez's low drive.
Niguez was then perhaps fortunate to only receive a yellow card for a studs-up challenge on Bale, before Real finally took the lead through Benzema in the 56th minute.
Ronaldo broke away down the left and delivered a low ball into the box, where David Lomban's attempted clearance ricocheted kindly off Tyton into the path of Benzema, who could not miss from a yard out.
And that advantage was doubled 13 minutes later as Isco got to the byline and dug out a cross from the left, which Ronaldo planted into the top left-hand corner with a powerful header from 12 yards.
The remainder of the game proved to be largely uneventful, as Real took full advantage of Barca's unexpected slip-up.