Martin Demichelis and Eliseu, with a penalty, earned Malaga the points as they were helped by a red card for Sevilla defender Federico Fazio in the 69th minute.
Malaga, who have qualified for the last-16 of the Champions League in their debut campaign, moved on to 28 points from 16 games, four behind third-placed Real Madrid.
Sevilla paid dearly for failing to convert early pressure into goals, in particular striker Alvaro Negredo who rounded the Malaga keeper only to fire against the post in the third minute.
Malaga scored with almost their first attempt just after half-time when Argentina defender Demichelis looped a header back under the bar at a corner, and Sevilla struggled to react.
Fazio brought down Joaquin as he raced into the area and was shown a straight red card, and Portugal's Eliseu sent Diego Lopez the wrong way from the ensuing penalty.
Sevilla lie 12th with 19 points, two behind Athletic Bilbao in 11th.
Bilbao were 1-0 winners at Real Mallorca, Getafe drew 1-1 at home to Osasuna, and Granada drew 0-0 at home to Real Sociedad.
Bilbao recovered from their midweek King's Cup humiliation to increase the pressure on Mallorca coach Joaquin Caparros.
Marcelo Bielsa's side, who reached the Europa League and King's Cup finals last year, were knocked out at home by third-tier Eibar on Wednesday, but took an early lead which proved to be enough at the Iberostar stadium.
EXTREME MEASURES
Striker Aritz Aduriz, again preferred ahead of disgruntled Spain forward Fernando Llorente, headed home after 11 minutes and took his tally for the season to 10.
Mallorca's Victor fired wide of an open goal in the second half, but they were unable to find away past Gorka Iraizoz and left the pitch to whistles after extending their poor run to 14 games without a win in all competitions.
"It's a challenge and I won't give up," Caparros told reporters.
"I know I have the backing of the board and the players and I am in debt to them as well as the fans. I have said on many occasions they will have to take extreme measures to get rid of me, because I will just keep getting back up again."
Osasuna were denied three points at seventh-placed Getafe by a disputed stoppage-time penalty.
Osasuna had Emiliano Armenteros sent off in the 77th minute but took the lead in a dull game when Kike Sola danced through the defence to score six minutes from time.
In the 93rd minute, Osasuna's Oier was judged to have handled the ball in the area, though television replays showed he had not, and Diego Castro netted the equaliser from the spot.
