Franco Zuculini tried his luck for Zaragoza from a narrow angle on 26 minutes, but failed to keep his attempt on target.
A minute later Alvaro Negredo shot wide for Sevilla from outside the penalty box, before Rodríguez forced Andres Palop into making a good save.
Then in the 36th minute Zaragoza took the lead, Postiga latching onto a Franco Zuculini pass and shooting home with his left foot from inside the penalty box.
The home side doubled their advantage on the stroke of half-time when Cristian Sapunaru headed home Rodríguez's delivery.
Zaragoza started the second half the brighter of the two teams, with Francisco Montanes and Apono trying their luck to make it 3-0 to their side.
However, Sevilla began to assert themselves on the match, Manu del Moral testing Gago from close range on the hour mark.
The visitors' pressure finally paid off in the 70th minute when they halved the deficit, Medel firing in from outside the Zaragoza box.
However, that proved to be a mere consolation, as although Baba came close to scoring the equaliser with 10 minutes left on the clock, Zaragoza held on for a 2-1 victory.