It was the home side who started the better and they might have taken the lead after 16 minutes when Allan Nyom ghosted into the box, but he fired his effort wide of the post.
Granada continued to create the better openings – and came close via Antonio Floro Flores after 40 minutes – but it was Deportivo who took the lead.
It was Nelson Oliveira who made the breakthrough as he struck from close range to send the away side ahead at the break.
Granada continued to push in the second period, and they got their reward ten minutes from time when Floro Flores converted from close range.
The result means that Granada remain in the bottom three, while Deportivo have continued their unbeaten start to the season.