Daniel Calvo had put Elche ahead just after the hour mark before the Frenchman scored twice in the last 20 minutes to give Madrid the win.
Elche came close to scoring several times with Thibaut Courtois forced into several fine saves.
Guido Carrillo nearly opened the scoring for Elche five minutes from half-time after Tete Morente dropped a ball into the box which he headed towards goal.
Madrid were made to pay for their missed chances when Calvo put Elche ahead with a header from a corner after 61 minutes.
However, their lead didn’t last long as Benzema pulled one back for Zinedine Zidane’s side just over 10 minutes later.
Substitute Luka Modric delivered a ball into the box and Benzema headed it in.