A goal from first-half substitute Nelson Oliveira looked to be enough for Deportivo to scrape past Granada, but for Antonio Floro Flores’s late equaliser.
In an uninspiring match, both teams probed but it was only when the visitors’ striker Riki went off injured that the game came to life.
Nelson Oliveira replaced the Spaniard with five minutes until the interval and quickly scored when miscommunication from defender Diego Mainz and goalkeeper Antonio Tono allowed him to steer the ball into an empty net.
The hosts struggled to find an equaliser, but on-loan Udinese forward Antonio Floro Flores managed to bundle the ball in with 10 minutes left to play.
Granada held on to pick up only their second point of the season, while Deportivo climb to six points continuing an unbeaten return to La Liga.