Bilbao's repeated attacks down the right side led to a corner kick by Markel Susaeta that Aduriz headed off Espanyol's Christian Stuani and into the net in the 29th minute.
Aduriz, just back from missing two games with a muscle injury, helped double the lead in the 44th when he gracefully dribbled through the defense before slipping a throughball for Borja Viguera to tap home.
Bilbao midfielder Ander Iturraspe scored from long distance in the 78th before Victor Sanchez got the visitors' consolation goal in the 84th.
Bilbao extended its unbeaten streak in the league to five games and rose into a provisional ninth place.
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