Facing the club he represented as both a player and a coach for the first time since taking charge of Barcelona, Valverde watched on as the talismanic Messi converted Jordi Alba's cut-back cross in the 36th minute to score his 12th LaLiga goal in 10 games this season.
The visitors needed a fine reactionary save from Marc-Andre ter Stegen to remain ahead before Paulinho secured the three points in stoppage time, tapping home the rebound after Luis Suarez's shot had been saved.
The Brazilian's strike condemned Athletic to an eighth straight league defeat against the Catalans, although it wasn't for a lack of effort against the unbeaten league leaders in Spain.
Still, Barcelona's hard-fought victory moves them four points clear of second-placed Valencia in the table and eight ahead of reigning champions Real Madrid, who now cannot afford any mistakes when they visit Girona on Sunday.
As for Messi, having begun the week by missing out to Cristiano Ronaldo for the Best FIFA Men's Player for the second year running, he ended it by once again underlining his importance to his club.
The Argentina international started and finished the move that gave Barca the lead at the end of an eventful first half. Having hit a first-time pass out wide to Alba, he ghosted beyond three static opponents to convert the return ball from his team-mate.
His first-time shot beyond Kepa Arrizabalaga made amends for an earlier miss, with Messi somehow hitting the post from close range with his right foot after waltzing around Athletic's goalkeeper.
Paulinho also struck the woodwork – sending a rising drive against the crossbar – but the hosts had their opportunities too.
The usually reliable Aritz Aduriz had two excellent chances in as many minutes as Athletic – held to a 1-1 draw by minnows Formentera in the Copa del Rey in midweek – produced a much-improved display for the visit of their former boss.
After a glancing header was comfortably saved by Ter Stegen, the veteran striker failed to convert when played through on goal, Barcelona's goalkeeper guessing correctly to keep out a curling effort low to his left.
However, Ter Stegen needed the bar to deny Raul Garcia's header early in the second half, as Jose Angel Ziganda's side started strongly after the break.
Unai Nunez produced two crucial blocks to prevent Barcelona from doubling their lead, keeping the result in the balance as the visitors visibly tired.
Inigo Cordoba volleyed over from a tight angle but Aduriz came the closest to grabbing an equaliser for Atheltic, his near-post header from a corner kept out by a diving Ter Stegen.
Instead Barcelona grabbed the game's decisive second goal in stoppage time, Messi leading a three-on-two counter that ended with Paulinho knocking the ball into an unguarded net with Arrizabalaga out of position.
