Youseff El Arabi cancelled out Gustavo Cabral's opener to secure the hosts half-time parity in Andalusia, but Fernandez's late tap-in snatched Celta victory against a side who are now one point below them in the league.
A 28th-minute header at the back post from Cabral put Celta ahead, but his goal came against the run of play as Granada had earlier come close to drawing first blood on two occasions.
Diego Mainz headed over the crossbar from a corner which had Yoel stranded, but the visiting keeper saved well from Yacine Brahimi's powerful drive shortly afterwards, and then denied midfielder Fran Rico.
Their pressure on the visiting goal finally paid dividends in the 41st minute as Rico's corner was glanced into the top corner by El Arabi, who has now scored eight goals in 19 matches this season.
An end-to-end second half yielded opportunities for both sides and eventually it was Luis Enrique's side who benefitted from the game being stretched. Fernandez was on hand to secure them a second straight win, burying the rebound after Roberto had parried Michael Krohn-Dehli's original shot.