An end-to-end game ensued with both teams concentrating on attack and the home side almost took the lead when Gonzalo Castro ran clear on the left, but after cutting inside he was denied by a last-ditch challenge from Ricardo Costa.
After a host of half-chances in the second half, the home side took the lead towards the end when Castro finished a blistering one-touch counter-attack with a low drive from the edge of the box.
As Valencia pushed for an equaliser, they were undone again on the break, this time it was Agirretxe whose shot deflected past Alves.
The away side did give themselves a lifeline with a minute to go when Jonas reacted quickest to head the ball in after Bravo parried it up in the air, but the scoring was not finished.
Valencia conceded again after a defensive mix-up allowed Agirretxe to run through unchallenged before chipping the ball over Alves to seal the win.