Julen Lopetegui's side fell behind in the first half when Ander Capa fired a shot past Yassine Bounou and into the top corner.
After the break, the visitors came out stronger and went close when Lucas Ocampos' close range effort was saved by Unai Simon.
Simon could do nothing to stop the equaliser that was eventually provided by Ever Banega, playing his final season in LaLiga Santander, who sent a freekick into the back of the net.
The Andalusians held on to preserve a victory that takes them six points clear of fifth placed Villarreal in the LaLiga Santander table.
The defeat for Athletic, however, means they lose ground in the hunt for the Europa League places and are now three points behind seventh placed Real Sociedad.