Zinedine Zidane’s men failed to convert a couple of good chances in the game, with Eden Hazard missing Real’s best opening.
Hazard, who was making consecutive starts for the first time since November, eventually limped off injured.
Levante grabbed the winner with 10 minutes left, as Jose Luis Morales crashed his effort past Thibaut Courtois from a narrow angle.
The result means Los Blancos are now two points behind rivals Barcelona who thrashed Eibar 5-0 earlier in the day.
