Pedro Morales gave Bernd Schuster's Malaga side the lead late in the first half but his wonderful strike was promptly cancelled out by a header from Gamerio.
Roque Santa Cruz then restored the visitors' advantage, but again Sevilla responded quickly through the former Paris St Germain hitman.
Unai Emery's side then had what would have been a winning goal wrongly disallowed for offside and, in the dying seconds of the game, Malaga captain Duda was sent off.
The two local rivals, neither of whom had showed much attacking ambition in their opening two Primera Division games, crossed swords to produce a chaotic encounter, which both began and ended in dramatic fashion.
Diego Perotti nearly caught Malaga goalkeeper Willy Caballero unawares after five minutes, the goalkeeper needing two attempts before he could gather the midfielder's shot from the edge of the area.
The visitors then created a clearer chance, with Morales forcing Javi Varas into a save, and Fabrice Olonga putting the rebound just wide of the far post.
Carlos Bacca then struck the woodwork on a rebound, after Caballero had kept out an effort from Alberto Moreno.
Centre-back Juan Cala missed a glorious chance to give the hosts a lead, shooting high over the bar at the far post following a cross from Gameiro.
The defender was made to regret the miss a few minutes later, when Morales put the visitors in front with a wonder goal. The midfielder picked the ball up in space in the Sevilla half and then continued advancing towards goal, unleashing a screamer into the top corner just before he got to the area.
Just two minutes later, however, Sevilla levelled.
Debutant Stephane Mbia, who joined last week on loan from QPR, crossed for Gameiro to head home, although replays showed the Frenchman had been in an offside position when the ball was played.
The hosts then passed up three opportunities to take the lead just before the half-time break, with Moreno narrowly missing the target before Caballero made a double save to thwart first Rabello and then Gameiro.
Cala almost put his side in deep trouble by playing a careless back pass towards Varas which Duda was inches away from pouncing on, but the goalkeeper was able to do enough to put the ball out for a corner.
With little over 25 minutes remaining, Santa Cruz put Schuster's men back in front.
The move began with a bursting run from Sergi Darder towards the box, the midfielder slipping the ball into the path of Santa Cruz, who shot first time low into the bottom corner beyond Varas.
But just a few minutes later, Gameiro struck again, taking advantage of a poor clearance from Sergio Sanchez to head the ball past Caballero.
Sevilla then thought they had scored the winner with six minutes remaining. Vicente Iborra headed the ball into the bottom corner but it was ruled offside as Gameiro had obstructed Caballero's view, but the Frenchman had in fact been played onside by Malaga midfielder Tissone.
There was still time for more drama, however. In injury time Vitorino Antunes sent a low cross into the box and Francisco Portillo slid to meet it but could only divert the ball wide of the far post.
And in the last minute, Duda was given a straight red card for a foul on Vitolo, which brought an attempted Sevilla counter attack to an end.