Sofiane Feghouli gave Valencia an early lead and although Celta equalised soon after through Michael Krohn-Delhi, the hosts claimed the points thanks to Aly Cissokho's 50th-minute winner.
Valencia, who have finished third in each of the last three seasons, had only managed to pick up two points from a tough start to the campaign which included trips to big two Real Madrid and Barcelona.
However, they notched up a first victory on Saturday against a Celta side who have now lost three of their four matches back in the top flight.
Los Che could hardly have asked for a better start as they took the lead inside four minutes with their first chance.
Celta threatened first with a 25-yard shot from Augusto Fernandez that Diego Alves did well to tip round the post, but moments later the visitors were behind when Feghouli slotted home right-footed from inside the box.
Celta battled back and Denmark international Krohn-Delhi equalised in the 15th minute with a close-range finish from Fernandez's pass.
Both goalkeepers made key saves to keep the scores level going into the break but Valencia were again quick out of the blocks at the start of the second period to re-take the lead - this time for good.
Dani Parejo sent over a cross from the left and Cissokho's header was too good for Javi Varas in the visiting goal.