Adrian claimed the points for Malaga as 10-man Sevilla lost their first game since April.
The former Deportivo La Coruna forward scored what proved to be the winner in the 16th minute and Malaga held out to end Sevilla's six-game winning streak.
The result takes recently-promoted Malaga up to sixth in the table with their fourth win of the season.
Sevilla coach Manolo Jimenez was boosted by the return of strikers Luis Fabiano and Ernesto Chevanton from injury, although Chevanton started on the bench with Jesus Navas in attack.
But Sevilla's treatment room still included the likes of Fredi Kanoute, Diego Capel, Javi Navarro, Arouna Kone, Aquivaldo Mosquera and Ivica Dragutinovic.
Malaga were also severely depleted with Salva Ballesta, Fabiano Rossato and Cheli out through injury and on-loan duo Lolo and Duda unable to play against parent club Sevilla.
The visitors rode their luck in the opening minutes when they failed to clear a corner and Navas' shot from 12 yards hit the post.
But Malaga took the lead in the 16th minute when Miguel Helder Rosario passed to Adrian who shot right-footed past Andres Palop in the Sevilla goal.
Adrian should have grabbed a second for himself and Malaga after 28 minutes but he failed to hit the target from 12 yards.
It could have proved costly as Sevilla raced down the other end and a chance opened up for Luis Fabiano.
The Brazil international, who struck 24 goals in 30 league appearances last season, looked rusty after his period out and lobbed the ball over the bar.
Navas and Renato had speculative efforts but neither were capable of testing Arnau from distance.
Renato came closer after the break but Arnau was more than equal to his effort and parried wide.
Malaga continued to keep their high-flying opponents at a distance and Arnau continued to deal comfortably with any long-range efforts.
Ndri Romaric's 30-yard free-kick was one such attempt that failed to push the Malaga keeper beyond his limits.
The game turned increasingly ill-tempered with the referee taking the names of Javier Calleja and substitute Chevanton, adding to Navas and Casaurang Nacho Verdes from the first half.
And in the 68th minute Adriano was dismissed for violent conduct after getting in a dust-up with Jesus Gamez.
The sending-off galvanized Sevilla, however.
Luis Fabiano, Navas and Chevanton all went close for the hosts in the next 10 minutes with Arnau tipping the best effort from Luis Fabiano around the post.
But the response was short-lived and Malaga had a flurry of late chances to seal the win.
Although Palop denied Albert Luque and Fernandez Fernando in the final minutes of the game, Malaga went onto claim all three points.
The victory will instill a much-needed belief for the newly-promoted side as they now face Sevilla, Barcelona, Real Madrid and Villarreal in successive games.
