The Europa League champions were two ahead by half-time at the Calderon but were made to sweat for their victory after a howler by goalkeeper Thibaut Courtois gifted the visitors a goal 10 minutes into the second half.
The win lifted Diego Simeone's side to fourth on 10 points from four matches, one behind Real Mallorca and Malaga, who have played one game more.
Leaders Barcelona are the only side to have won all five matches following Saturday's 2-0 success at home to Granada and lead by four on 15 points.
Champions Real Madrid, who have taken only four points from their opening four outings, were due to play at city rivals Rayo Vallecano in Sunday's late kick-off but their game was abandoned in bizarre circumstances.
Valencia had their chances but Mallorca's Israel goalkeeper Dudu Aouate was on superb form and produced several fine saves to deny the visitors.
The former Inter Milan and Newcastle player, who joined Levante this month on a free transfer from Russia side Rubin Kazan, left his marker for dead and slotted past Claudio Bravo after Jose Javier Barkero's 70th-minute penalty had cancelled out David Zurutuza's strike in the 23rd minute.
