Jose Luis Morales scored after 79 minutes just the hosts' second shot on target. To make matters worse, Los Blancos also lost Eden Hazard, who limped off with an ankle injury in the 67th minute.
Los Blancos drew with Celta Vigo in their previous outing and are now two points behind Barcelona after they beat Eibar 5-0 earlier in the day.
Levante were happy to sit back and hit the visitors on the counter, and Los Blancos struggled to break down the defensive block during the first half.
Karim Benzema side-footed a ball wide of goal after 11 minutes, and Casemiro headed the best chance of the half wide five minutes later. Goalkeeper Aitor Fernandez did not clear a corner well, but the Brazilian's aim was off.
Apart from those two chances, Levante didn't give away much. As The Spanish Football Podcast's Twitter account pointed out, that wasn't a surprise:
There were a few half-chances for Luka Modric and Isco, with the latter setting up the former on the edge of the box late in the half. His shot was fired straight at Fernandez, however.
Marcelo nearly picked out Benzema to close out the half, but the defence stood firm and didn't let him get his shot off.
At half-time, La Liga Lockdown noted the visitors had dominated possession:
La Liga Lowdown 🧡🇪🇸⚽️ @LaLigaLowdown
It’s all tied here in the Estadio Ciudad de Valencia. Real Madrid dominating possession for the most part in the first half but Aitor Fernández continues to be a rock at the back for Levante ❌ Still 0-0 but can Levante hang on for another 45 minutes? #LLL 🧡🇪🇸⚽️ https://t.co/lAXm0HftE4
Levante started the second half well and created a good chance for Enis Bardhi, who curled a shot wide. Real soon got back on the front foot, however, and Eden Hazard could have opened the scoring but for Fernandez.
Thibaut Courtois made an excellent save to keep out a deflected effort from Jose Campana, before compatriot Hazard made his way off the pitch with a visible limp:
Los Blancos had struggled to create much with their star forward on the pitch, and things didn't improve when he came off.
They then fell behind when Morales chased what seemed a hopeless ball over the top before firing a first-time strike from a tight angle, catching Courtois out at his near post.
While it was a great strike, the stopper pulled his arms back because he appeared to think the ball was going over:
Real seemed shocked by the sudden turn of events and never threatened an equaliser. The best chance fell to Borja Mayoral, who nearly scored against his parent club before Raphael Varane made a crucial block. He was also involved in a late incident with Dani Carvajal over time-wasting.
Los Blancos' last chance came via Sergio Ramos, but he aimed his header straight at Fernandez.
Real host Manchester City in the UEFA Champions League on Wednesday before hosting Barcelona on March 1. Levante face Eibar in La Liga next Saturday.