The hosts pressed and probed for the opening 20 minutes but their attacks were being kept at bay by an alert Levante defence.
Indeed, despite the hosts' dominance with the ball, it was the away side who went ahead just after the half-hour mark when Michel slalomed his way into the box before finding the bottom corner.
However, five minutes later Real were back level through a superbly controlled volley from Gonzalo Higuain.
Five minutes into the second half it could have become 3-1 for Madrid, but Higuain was just unable to direct Luka Modric's effort on target.
As the game started to stretch, it was Madrid who scored the crucial fourth goal as Cristiano Ronaldo thumped a half-volley into the top corner.
In the closing minutes Mesut Ozil turned a Ronaldo cross into the empty net to make it 4-1 and then added another in stoppage time to complete the rout.