Substitute Antoine Griezmann scored the game’s only goal midway through the second half when his deflected shot bobbled past Valencia goalkeeper Giorgi Mamardashvili.
Griezmann and Yannick Carrasco both had chances to extend Atlético’s lead late in the game, but their efforts were well saved by Mamardashvili.
The result leaves Atleti sixth in La Liga, three points behind leader Real Madrid having suffered a 2-0 home defeat against Villarreal in the second round of games.
An eventful first half saw several VAR interventions — first when Valencia’s American midfielder Yunus Musah had a goal ruled out following a foul on Joao Félix in the buildup, then when a red card for Thierry Correia was downgraded to a yellow.
Atlético also had chances in the first half when Valencia gave away the ball at the back, but Álvaro Morata and Félix both saw their shots saved by Mamardashvili.
The arrival of Griezmann and Thomas Lemar in the second half, however, swung the game in Atlético’s favor, and it was Lemar’s surging run and pass that set up the winning goal.
Valencia is now 14th in La Liga having not won since its opening game of the season against Girona, but Gennaro Gattuso’s side will be bolstered by the arrival of Edinson Cavani, who watched on from the stands during Monday’s defeat.
The Uruguayan international joins Valencia until June 2024 having left Manchester United last season.
After stints at Palermo, Napoli, and Paris Saint-Germain, this will be the first time the 35-year-old Cavani has played club football in Spain.
“I think my coaching staff and medical staff have to work well because he is a player who has only trained alone for the last three months,” Gattuso told reporters after the defeat.
“We have to coach him well. He has come to help, but we have to help him with his play and organization.”