Valverde has now overseen 12 wins and a draw from his first 13 La Liga and Champions League matches as Barca reestablished their four-point lead at the top of the table over Valencia, who beat Alaves 2-1 earlier on Saturday.
The Catalan giants also move eight points clear of rivals Real Madrid, who are in action on Sunday amidst a backdrop of political turmoil as they travel to Catalonia to take on Girona.
For once in recent weeks, Barca were afforded a break from the political spotlight on their trip to the Basque Country with the Estelada flag in favour of Catalan independence scattered among the home fans as well as the travelling support.
Valverde left Bilbao in the summer and his impact has been felt just as much in Bilbao as it has in Barcelona -- Athletic have now one just one of their last 12 matches in all competitions.
But the hosts started the brighter and only a stunning save from Marc-Andre ter Stegen prevented Aritz Aduriz from slotting Athletic in front on 19 minutes.
Barca, and Messi in particular, grew into the game as the half wore on and the Argentine should have opened the scoring when he hit the woodwork for already the 10th time this season with the goal at his mercy from Luis Suarez's pass.
Messi was at the heart of another flowing team move to break the deadlock eight minutes before half-time. He exchanged one-twos with Paulinho and Jordi Alba before sweeping home the left-back's low cross.
Paulinho should have extended the visitors' advantage when he smacked the crossbar moments later, but an under-par Barca had to withstand plenty of Athletic pressure after the break.
Raul Garcia's header also hit the woodwork, while Ter Stegen produced another stunning stop from Aduriz five minutes from time.
Barca even resorted to wasting time in the final quarter, but held out to record a ninth clean sheet in their last 13 games.
And they added a second deep into stoppage time when Paulinho tapped home the rebound after Kepa Arrizabalaga had parried Suarez's first effort.