Their lead lasted for less than a minute though, as Roque Santa Cruz set Pablo Perez up for the equaliser.
Perez had a chance to put Malaga ahead early in the second half, but his long-range effort failed to find the target.
Espanyol regained the lead inside the final quarter of an hour when a fast break from Garcia set up Pizzi to power the ball home with a curling effort.
The home side's chances of getting back on level terms were dealt a blow less than two minutes later when Perez picked up his second yellow card of the night, leaving them a man short for the final 10 minutes.
Oleksandr Iakovenko came close to levelling the scores late on, but his finish provided an easy save for Francisco Casilla.