The fate of both sides had already been confirmed well before the final weekend, as Los Che were guaranteed to end fourth and their opponents could finish no higher than 18th.
The breakthrough goal arrived just short of the half-hour mark, Zaza celebrating his Italy World Cup call with a low shot from inside the box that crept in at the far post.
Parejo and Rodrigo both tried their luck either side of half time, while Maksimovic climbed highest to meet a corner and saw his effort skim the top of the crossbar.
After Zaza became the second home player to hit the frame of the goal, Guedes had a long-range effort pushed around the post and then stabbed home from his next chance.
Perez did manage to pull one back 10 minutes from time with a simple finish from 10 yards, before Juame produced a couple of smart stops to help his side hold on for all three points.
VALENCIA (4-4-2): Jaume; Vidal, Garay, Murillo, Gaya; Carlos Soler, Parejo (Kondogbia 62'), Maksimovic, Guedes; Rodrigo (Vietto 67'), Zaza (Mina 64')
DEPORTIVO LA CORUNA (4-2-3-1): Koval (Tyton 83'); Juanfran, Mujaid, Navarro, Luisinho; Krohn-Dehli, Mosquera; Valentin (Adrian 62'), Emre Colak, Bakkali (Perez 59'); Borja Valle