The visitors bossed possession and had the better of the first half, but Borja Iglesias’ 41st minute header was enough for Espanyol to record their sixth win of the season and move to within three points of leaders and rivals Barcelona.
The three points did not come easily though, with Bilbao dominating possession and having plenty of chances.
Mikel San Jose had a chance before Espanyol’s first chance came in the 36th minute, when Iago Herrerin got down low to save Sergio Garcia’s shot.
They had more luck with their second opportunity though as Iglesias headed home Didac Vila’s cross for his fourth goal in his last three league matches.
Athletic almost hit straight back but Inaki Williams’ shot struck the post two minutes later.
The visitors launched a late volley of attacks, with Unai Nunez, Williams and Inigo Martinez all going close in the last 10 minutes, but Espanyol hung on.