Barca were in cruise control in the first half and went into the break ahead courtesy of Alcacer's opener and Messi's sweet strike.
Ahead of the contest, Blaugrana boss Ernesto Valverde claimed his side were down to the "bare bones"; however, that did not stop the hosts asserting their dominance early on, with Alcacer making their pressure count inside eight minutes.
Philippe Coutinho was inches away from doubling Barcelona's lead moments later when he met another Alba cut-back with a volley which crashed back off the crossbar.
After extending their advantage, Barca continued their dominance, with Coutinho's hitting of the woodwork for the second time of the afternoon swiftly followed up by Paulinho being denied via the same obstacle.
The second half was played at nearly a testimonial pace with Barcelona content to knock the ball around at their leisure. After being teed up just outside the box, Messi unleashed an unstoppable shot into the bottom-right corner.
Tottenham flop Paulinho was then the latest player to have his head in his hands, after his strike smashed against the post in the 44th minute to cap a dominant, but frustrating half for the Catalan club.
Messi almost handed Barca the lead after four minutes but his curling free-kick was tipped away by Bilbao shot-stopper Kepa Arrizabalaga.
Bilbao started off the second period on the front foot, with Inigo Lekue pulling a shot wide from 25 yards out, before Sabin Merino spurned two opportunities to pull a goal back for Jose Angel Ziganda's side.
Messi looked to add some spark in the 88th minute, embarking on a solo run and firing across the face of goal.
The unbeaten league leaders slowed down in the second half and Athletic came into the game for the first time but despite numerous forays into Barca's area they rarely got close to troubling goalkeeper Marc-Andre ter Stegen.