It marked the first time since 2015 the Galician club has won their first two matches of the season, handing Valencia a second straight loss in the process.
Celta's captain and talismanic striker Iago Aspas was again at the heart of events on Friday. He scored for the second game in a row and then missed a penalty shortly before half-time.
Diego Lopez had put Valencia ahead after 14 minutes when he converted from close range after a goalmouth scramble, but Celta equalised midway through the first half when Oscar Mingueza volleyed home to complete a neat team move.
Aspas's goal came five minutes later when the 37-year-old forward took a weighted through ball from Mingueza and finished perfectly into the bottom corner.
Valencia keeper Giorgi Mamardashvili then saved Aspas's spot kick in first-half injury time, but Fran Beltrán added the third goal on the hour mark with a classy strike from the edge of the penalty area.
Valencia's run of nine games without a win - dating back to last season - is their worst under one coach since Gary Neville led the club in 2016. And they face a difficult third match next week at Athletic Bilbao's San Mamés arena.
"The team is hurting," said Valencia midfielder Pepelu. "We don't want to look at the fixture list. It's up to us to go to the San Mamés and compete."
In Seville, Ayoze Pérez slotted home a volley in the fifth minute of injury time to give Villarreal a 2-1 win over Sevilla.
The visitors took the lead with their first attack of the match after just one minute as Arnaut Danjuma, who also scored early against Atletico Madrid in the opening round, netted with a poised finish from 15 yards out.
Sevilla's equaliser came in first-half stoppage time when Dodi Lukebakio controlled a long pass and volleyed home.
Both sides had goals disallowed after video reviews before Pérez's late winner for Villarreal.
The result gave Villarreal four points from two games, while Sevilla have one point.
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