Markel Susaeta gave the visitors the lead on 28 minutes, but just moments later Patrick Ebert levelled.
Iker Muniain restored Athletic's advantage five minutes after the re-start, and the Basque side held on for the remainder of their game to start the campaign on the right foot.
Valverde appears to have kept many remnants of the team's style under his predecessor Marcelo Bielsa, and his side played attractive, attacking football while retaining their aggression.
Their first real attempt came when Ander Herrera slid a ball through to Susaeta, who cut in from the left-hand side towards goal but pulled his shot just wide of the near post.
Not long after, Susaeta did hit the target, rounding off a superb team move to give his side the lead.
Andoni Iraola played a low pass into the area, Herrera pulled off a spectacular backheel to send the ball to Benat, who then found Susaeta to drill the ball into the bottom corner.
Valladolid's reply was immediate. Javi Guerra played Oscar Ramos in down the right-hand side, and the midfielder battled with an Athletic defender to play the ball across to Ebert, who gave Athletic goalkeeper Gorka Iraizoz no chance with a clinical low finish.
Athletic's second goal again came from a move started by Iraola.
The full-back sent a high cross into the danger zone which caused problems for Valladolid centre-back Marc Valiente, who diverted the ball onto the post. It rebounded back right into the path of Muniain, who gratefully bundled it into the net.
The 20-year-old has now scored as many goals as he did the entirety of last season.
Valladolid's best chance to get back into the game came from an unlikely source - former player Mikel Balenziaga.
The left-back, who was making his debut for Athletic, almost scored an own goal, kneeing the ball just a couple of feet wide of the post as he tried to clear a cross from the left from Carlos Pena.
Another debutant, Kike Sola, was denied a goal by Valladolid goalkeeper Diego Marino, who punched clear his effort from outside the area, while Herrera struck the post later on.