Sergio Busquets' suspension paved the way for Miralem Pjanic to return, while captain Lionel Messi was introduced ahead of Martin Braithwaite following last Sunday's win away to Elche in the league.
Messi looked to hit the ground running from the get-go after he ran down the far side of the area to force Bilbao goalkeeper Unai Simon into a one-handed save from a close-range shot.
It wasn't long before the skipper put the Blaugarana ahead from a free-kick that found the top corner, bringing up his 650th goal for the clb.
Ronald Araujo almost had the host two goals up close to halftime from a drop of the shoulder into the area following a marauding run, but in the end fluffed his lines.
After a dominant opening spell, Barcelona were pegged back five minutes from the restart in fortuitous fashion as Jordi Alba directed a cross from Raul Garcia into his own net.
The Blaugrana were almost back in front also from an own-goal 57 minutes gone, but Simon reacted smartly to smother Inaki Williams's header following a cross by Messi.
Simon was at it again a minute later when he produced a powerful save to parry an equally powerful strike from the cusp of the area by Pjanic.
The Catalans eventually regained the lead with 15 minutes to go after Antoine Griezmann tapped a low cross from Oscar Mingueza into the far corner of the net.
Barcelona ran down the clock seven from time with the introduction of Clement Lenglet for Griezmann, as Bilbao targeted a comeback however 2-1 was how it finished, with the Catalan giants leapfrogging Real Madrid into second spot.