The result has moved Depor into sixth position in the table, while Espanyol have dropped to ninth following a third defeat of the new campaign.
The contest continued to flow from end-to-end as play developed, but it was Depor that scored the game's second goal. Luis Alberto did brilliantly to find space outside the box before feeding Perez, who dispatched his effort into the bottom corner for 2-0.
The visitors remained a threat though and hit the post through Pape Diop in the latter stages of the first period in La Coruna.
Depor put the game to bed early in the second period, however, when Celso Borges set up Perez for the attacker's second of the game. The hosts continued to dominate and had a golden chance to make it 4-0 in the 64th minute, but Oriol Riera struck the crossbar from close range.
It got worse for Espanyol late on as they were reduced to 10 men following a red for Diop on what was a miserable afternoon for the visitors.