The Europa League champions were two ahead by halftime 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.
Mallorca inflicted further pain on struggling Valencia when they beat them 2-0 at the Iberostar Estadi before Malaga were held to a 0-0 stalemate at Athletic Bilbao.
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 kickoff but their game was abandoned in bizarre circumstances.
With the game due to kickoff at 9.30 p.m. local time and the stadium in semi-darkness, Rayo president Raul Martin Presa told Spanish television unidentified persons had cut the cables on some of the lights.
Discussion were underway to try to rearrange the game for Monday, he added.
Mallorca continued their impressive early-season run and condemned Valencia to a second defeat in five days thanks to goals from Victor Casadesus and Javier Arizmendi.
Casadesus put the Balearic Islanders ahead in the eighth minute before Arizmendi, a former Valencia player, doubled their lead 10 minutes into the second half and moments after coming off the bench.
Valencia had their chances but Mallorca's Israel goalkeeper Dudu Aouate was on superb form and produced several fine saves to deny the visitors.
Valencia, who lost 2-1 at Bayern Munich in their Champions League Group F opener on Wednesday, are 14th on five points.
New signing Obafemi Martins was a hero on his debut for Levante when the speedy Nigerian came off the bench to net a scorching 86th-minute winner in a 2-1 comeback win at home to Real Sociedad.
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.