The teams had drawn 1-1 in the first leg, with Malaga advancing courtesy of a 4-1 victory in tonight's encounter at the Estadio La Rosaleda.
The hosts started brightly in the opening 10 minutes, but fell behind when Ruben Arroyo scored against the run of play.
Malaga went close again after the break, but Sebastian Fernandez could not capitalise on Boveda's mistake.
Saviola was then frustrated by the crossbar as Eibar continued to ride their luck.
The visitors' resistance lasted until the 74th minute. It was Diego Buonnanote who found the leveller, before Fernandez struck three minutes later to turn the tie completely on its head.
Francisco Portillo then managed to get himself on the scoresheet with eight minutes remaining, before Guille Roldan saw red for a reckless challenge on Fernandez.
Eibar's misery was complete when Buonnanotte claimed his second of the game deep into injury time.