Tommer Hemed came close to putting Almeria ahead at the start of the second half, but his swerving short from the edge of the box was well saved.
The visitors were able to capitalise on the miss a few minutes later when an Aritz Aduriz corner fell for Xabier Etxeita to smash in from close range.
Oscar de Marcos tried to get forward to slot in a second a couple of times for Bilbao, but he was caught offside twice while looking for the goal.
Meanwhile Thievy attempted to force in an equaliser just a couple of minutes from full time, but his effort failed to trouble the keeper.
The result lifts Bilbao up to 14th in the table, just one place behind Almeria.