All five goals came in a topsy-turvy opening 33 minutes with the game settling down only after Malaga's Portuguese forward Eliseu was sent off in the 41st, allowing the visitors to take control.
Villarreal continued their strong start to the campaign, racking up their fourth consecutive league win to move on to 12 points from five matches, one short of leaders and near neighbours Valencia.
Barcelona are third on goal difference, with Real Madrid fourth on 11 points.
Eliseu gave Malaga a fourth-minute lead after a free-kick but two goals in three minutes turned the game on its head, Cazorla firing in a deflected shot and Italy's Giuseppe Rossi netting a fine solo effort in the 24th.
Jose Rondon headed Malaga level in the 30th after good work from Quincy Owusu-Abeiye down the left, but the score changed again after only a few minutes.
Cazorla, who missed out on Spain's World Cup finals squad because of an injury-interrupted season last year, proved he was back to his best with a superb winner cracked in from outside the area.
Just before the break, Spain defender Carlos Marchena got Eliseu sent off after theatrically falling to the ground clutching his face as the two went forehead to forehead.
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