Celta held Ernesto Valverde's side at bay until the third minute of added time when Joao Pereira floated a cross to the back post and Valdez, who had only been on the pitch a few minutes, nodded powerfully past Javi Varas.
The victory came at a cost, however, as Valencia lost Aly Cissokho to injury when the fullback went over awkwardly on an ankle and had to be replaced towards the end of the first half.
Valencia, who host PSG in their last 16 first leg on Tuesday, are fourth on 37 points from 23 games, one ahead of Malaga who play at Levante later on Saturday (1900 GMT).
Stuttering champions Real Madrid can trim the gap with second-placed city rivals Atletico to four points with a win at home to Sevilla in a later kickoff (2100).
Atletico visit Rayo Vallecano on Sunday (2000) after Barcelona, who are nine points clear at the top, host Getafe (1100).
Real Mallorca's new coach Gregorio Manzano, appointed this week to replace the sacked Joaquin Caparros, began his third stint at the Balearic Islands club with a 1-1 home draw against fellow strugglers Osasuna.
Osasuna midfielder Lolo headed in from a corner in the 77th minute but Pedro Geromel equalised in added time to leave Mallorca in 19th place on 18 points. Osasuna are 17th on 22 points, two ahead of Celta in 18th.
- Sports & Recreation