Toni Kroos had Madrid's first chance of the evening, but after being picked out on the edge of the box he fired a strike wide of the post.
Soon after, the visitors were awarded a controversial penalty when Cristiano Ronaldo was adjudged to have fouled Pedro Mosquera inside the box as he tried to clear the ball.
Elche captain Albacar stepped up to the spot and made no mistake with a composed finish into the top corner.
The referee then awarded Madrid a penalty after Mosquera brought down Marcelo inside the box and Ronaldo converted from the spot.
Ronaldo scored his second of the match four minutes later when he connected with Marcelo's cross, before planting a header into the corner of the net.
The Portuguese came close to a third goal when his powerful free kick was beaten away by Herrera and moments later the keeper denied a close-range attempt from Kroos.
After the break Coro attempted to pull a goal back for Elche, but he could only fire a strike just wide of the top corner.
Madrid continued to dominate the match, but it took them until the final 10 minutes to further extend their lead.
They were awarded their second penalty of the evening when Ronaldo was tipped by Mario Pasalic and the Portuguese made no mistake by scoring from the spot to complete his hat-trick.
In stoppage time Ronaldo grabbed his fourth goal of the evening when he was played through by Bale and slid an effort into the corner to complete the rout.