David Timor's first-half opener was cancelled out in the second half by Djene's own goal following a blunder by goalkeeper David Soria, whose hands were again shaky as Carlos Fernandez struck the winner with 11 minutes left.
Granada moved up a place to eighth on 41 points.
After a lengthy suspension of the Spanish league due to the COVID-19 crisis, the game got off to a slow start but Getafe went ahead in the 20th minute when Timor curled a fine shot under the bar from just outside the area.
Granada hit back after 70 minutes when Djene chested the ball into his own net after Soria failed to handle a bouncing free kick from Fede Vico.
The home side doubled their tally nine minutes later as Fernandez fired home after his first attempt was parried back into his path by Soria.
Sevilla beat Real Betis 2-0 on Thursday to reach 50 points and tighten their grip on third place. (Reporting by Julien Pretot; Editing by Ken Ferris)