The visitors were lucky to be on level terms at the break after Alvaro Negredo hit the post for a dominant home side after just two minutes.
And Sevilla paid for their profligacy in the second period as Martin Demichelis headed Malaga in front and Eliseu made it 2-0 from the penalty spot after Federico Fazio saw red for bringing down Joaquin Sanchez.
Sevilla were well on top in the first half and should have been in front inside three minutes.
Negredo showed good determination to get in between two Malaga defenders and onto a hopeful ball forward, before rounding the onrushing Willy Caballero.
However, that pushed the striker slightly wide and his right-footed shot bounced back off the post and straight into the arms of a grateful Caballero.
Negredo then forced a decent save from Caballero on 14 minutes and Jesus Navas' follow-up was deflected wide for a corner as Sevilla pushed for the opening goal.
Malaga certainly did not look like finding the net, failing to manage a single effort on target in the opening 45 minutes.
The visitors quickly made amends for that on the resumption, taking the lead just three minutes into the second period.
Sanchez's corner from the left found Demichelis climbing highest at the back post and he looped a header back into the far corner despite Negredo's best efforts to keep the ball out.
Sevilla were stunned and their misery was complete in the 69th minute when referee Miguel Gamez had no hesitation in sending off Fazio for a professional foul as Sanchez bore down on goal.
Eliseu sent the goalkeeper the wrong way from the spot to double Malaga's lead and the visitors looked the more likely to score again as Sevilla pushed forward trying to get back into the game.