Los Che controlled much of the match at the Balaidos, but looked to be heading for just a point until Valdez, who had only been on the pitch for five minutes, headed home a Joao Pereira cross in injury-time.
The result lifts Valencia ahead of Betis into fifth place, with Verdiblancos hosting Valladolid on Sunday night, and gives Valverde's team a welcome boost ahead of their Champions League tie with Paris Saint-Germain this week.
“As the game progressed I thought we really took control," he said.
“We had hope right until the end, but it did look for a while like it would end 0-0. When we did score, it was obviously hard on Celta, but for us it was brilliant.
“It was a complicated match and I'm glad we've managed to come away with the three points.”
However, the three points came at a cost as defender Aly Cissokho went off injured shortly before the end of the first half, making him a doubt for Wednesday's Champions League clash.