Valencia took an early lead through Fabio Aurelio. Deportivo came back with a Donato header just after the break but Aurelio grabbed the winner with a run and shot in the 62nd minute.
Deportivo continue to lead the standings with 66 points from 34 games but Real Sociedad, also on 66 points, and Real Madrid, third on 65, will both have the chance to overtake them on Sunday.
Real Sociedad are at home to Recreativo Huelva, while Real Madrid host Malaga at the Santiago Bernabeu.
Both Real Sociedad and Real Madrid have five games left to play, while Deportivo have four.
Valencia's victory takes them above Celta Vigo and into the fourth and final Champions League qualification place.
