Goals from Simone Zaza and Daniel Parejo either side of an Iago Aspas strike saw Marcelino's men return to winning ways and stay three points clear of third-placed Real Madrid in addition to moving within striking distance of Barcelona, who are not in action until Sunday.
Celta, meanwhile, remain 10th in the table having suffered only their second defeat in their last six outings across all competitions.
The hosts, who only fell to their first defeat of the season last weekend, almost produced a perfect reaction to losing their unbeaten record after just two minutes when a corner fell to Ruben Vezo, who saw his subsequent effort come back off the post.
Celta also threatened an opening goal in the early stages of the match too, though, with Pione Sisto coming closest for the visitors when his shot from the edge of the area went narrowly wide of the target.
Valencia were soon back on the attack and Simone Zaza needed to be denied by Ruben Blanco at the end of a mazy solo run before Carlos Soler placed an effort just past the post midway through the first half.
Zaza then came close again and was only denied by a fine Blanco save shortly before the half-hour mark, although there was nothing the Celta keeper could do from the resulting corner as Zaza darted to the front post and glanced home his 10th goal of the season.
Another former Premier League flop turned La Liga goalscorer was next to come close when Aspas had his first sight of goal, but his header was tipped over the crossbar by Neto.
Valencia held on to their lead heading into half time, but within a minute of the restart parity had been restored as Aspas made it nine goals in his last eight La Liga games, reacting quickest inside the box to convert a loose ball after a deflection had fallen kindly for him.
It looked as though the hosts might be on course to drop more points in the title race, but they were given a helping hand with only 10 minutes remaining when Hugo Mallo was penalised for a foul inside the area.
Blanco guessed the right way from the resulting spot kick and even managed to get a hand to the ball, but Daniel Parejo's penalty had enough on it to restore Valencia's lead.
Indeed, that proved to be enough to hand the hosts all three points as they kept up their title challenge between the two usual heavyweights of Spanish football by returning to winning ways at the first time of asking.
Valencia (4-4-2): Neto; Montoya, Gabriel, Vezo, Gaya; Soler (gil, 61'), Parejo, Kondogbia, Pereira (Maksimovic, 89'); Zaza, Rodrigo (Mina, 66')
Celta Vigo (4-3-3): Blanco; Mallo, Cabral (Guidetti, 84'), Fontas, Castro; Wass, Lobotka, Hernandez; Aspas, Gomez, Sisto (Mor, 82')