Dani Parejo and Paco Alcacer struck for Nuno Espirito Santo's men as they moved eight points clear of Sevilla in fifth, who host struggling Elche on Sunday.
Valencia piled pressure on in the first half, but were unable to find a way past Fabricio in Deportivo's goal.
But their pressure paid off after the break as Pablo Piatti proved too tricky for Juanfran in the penalty area and a foul on the Argentinian allowed Parejo to break the deadlock from 12 yards.
Piatti was again involved as Alcacer made the points safe by prodding home Sofiane Feghouli's cut-back from three yards out - the Spain striker's first goal of 2015.
Defeat leaves Deportivo nervously looking over their shoulders, just a point clear of 18th-placed Almeria.
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