The result is the perfect springboard for Ernesto Valverde's side ahead of their Champions League match with Paris St Germain on Tuesday but it means that the Galicians are condemned to spending another week in the relegation zone.
Although the goal came late, Valencia were worthy winners of the game overall as they created the greater number of chances and had a goal wrongly ruled out for offside early in the second half.
However, Celta will still be ruing their luck at having missed three clear chances to score before conceding so late on.
Valencia have been in resurgence since Valverde took over from Mauricio Pellegrini in December and, buoyed by drawing with Barcelona the previous weekend, began the game strongly.
Full-back Aly Cissokho was asking plenty of questions of the hosts down the left-hand side until he was forced to retire from the game with an ankle injury on 36 minutes.
But Celta created the first clear opening, with Iago Aspas missing a great chance to give his side the lead, racing onto a pass by Fabian Orellana and opting to chip Valencia goalkeeper Vicente Guaita, but placed his shot just wide of the left post.
The chance sparked brief a period of Celta domination and only a great save by Guaita prevented Iago Aspas from scoring after half an hour.
Just moments earlier Vadim Demidov had to clear the ball off the line to prevent Tino Costa from scoring, and Adil Rami squandered a glorious chance to score on the stroke of half-time when he headed Tino Costa's cross onto the post.
Roberto Soldado looked to have given the visitors the lead moments into the second half but saw his goal ruled offside. The striker was furious with the decision and replays showed he was in line with the defence when the ball from Ever Banega was played.
Michael Krohn Dehli fired a shot just wide of goal not long afterwards, and then Valencia did all the attacking. Javi Varas made two great saves to keep the score level, first from Jonas from the edge of the area, and then from a header by Sofiane Feghouli in stoppage time.
But unfortunately for Paco Herrera's side, there was nothing he could do to prevent Valdez's winner.
The Paraguayan replaced Jonas with just two minutes remaining of normal time but he made the most of the few minutes he had on the pitch, meeting a perfect cross from Joao Perreira with a header at the far post to snatch the points for Valencia.