Valencia were level after 63 minutes, however, when Nelson Valdez found the bottom corner following a sweeping move.
There was time for late drama as Ricardo Costa headed a late winner for the away side, with Deportivo ending the evening with nine men.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
DEPORTIVO: Aranzubia; Ze Castro, Pablo, Aythami, Silvio; Assuncao, Bergantinos, Santos; Riki, Gama, Pizzi
VALENCIA: Alves; Costa, Rami, Pereira, Ruiz; Guardado, Banega, Costa; Valdez, Jonas, Piatti