Celta held Ernesto Valverde's team 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, though, 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 Champions League last 16 first leg on Tuesday, have 37 points, two ahead of Real Betis, who host Real Valladolid on Monday.
"The match was heading for 0-0 and it was cruel on Celta," Valverde said.
"We played a balanced first half and we hit the post at the end but in the second half slowly things started to go our way," he added. "They suffered more from the effort."