Real Sociedad recorded their first away victory of the season with a vital 2-1 victory in La Rosaleda.
It is the second straight defeat for Málaga in the league, having lost by the same scoreline to Rayo Vallecano last weekend.
Carlos Vela gave the visitors a surprise lead in the opening minute of the game, firing home after a pass from Diego Ifrán, but Màlaga levelled through Javier Saviola with less than ten minutes before half-time, scoring on the rebound after Joaquín's shot was blocked.
Màlaga looked the side more likely to score the next goal but La Real also posed a threat, which bore fruit after 60 minutes with Xabi Prieto showing nerves of steel to calmly take the ball round Willy Caballero after receiving a short pass from Diego Ifrán.
Málaga then pushed for an equaliser, with Isco coming closest to scoring but his shot was saved by Zubikarai.
The result means Philippe Montanier's side are now out of the relegation zone and 13th in the league table, while Málaga missed a chance to leapfrog Real Betis in fourth place, and remain in fifth.