Bilbao is sixth in the standings on 16 points, one less than fourth-place Villarreal. Barcelona leads the standings on 25 points after nine matches, ahead of Atletico Madrid on 24, two more than third-place Real Madrid.
Also, Levante beat Celta Vigo 1-0 after a goal by Papakouli Diop.
Celta had dominated most of the match when, against the flow of play, Diop connected with the ball after it rebounded off the wall from a free kick taken by Juan Francisco Garcia in the 89th minute.
"We found ourselves with that goal which, well, I don't know if we deserved it or not, but no one can take it off us now," said Garcia, adding that the weather conditions on the field had been very difficult due to heavy rain.
Levante goalkeeper Keylor Navas had saved a low shot by Danish forward Michael Krohn-Dehli in the 12th minute and was again in action in the 40th when he parried Antonio Rodriguez's shot.