Depay fired home four minutes into stoppage time to put Lyon on 48 points from 22 games with PSG, who were without the injured Neymar, on 56 after their second defeat of the season.
Dani Alves was shown a straight red card in the 57th minute after a rough tackle on Tanguy Ndombele. Layvin Kurzawa had cancelled out Nabil Fekir's early opener.
Monaco are fourth on 46 points after goals by Jorge, Rachid Ghezzal and Rony Lopes gave them a 3-1 home win against 10-man Metz.
In Lyon, PSG were caught cold in the second minute when Fekir opened the scoring with a splendid free kick from 30 metres.
The visitors dominated possession but clearly lacked the speed and craft of Neymar, who missed the game because of a thigh injury.
Kylian Mbappe was taken off on a stretcher after colliding with Lyon keeper Anthony Lopes but PSG's club doctor Eric Rolland said it was "nothing serious".
PSG equalised four minutes into stoppage time as Kurzawa unleashed a brutal volley that went under the bar from Alves's cross.
The Brazilian was then sent off for his tackle on Ndombele and PSG cracked at the last moment when Depay unleashed a powerful shot that went into the top corner.
(Reporting by Julien Pretot, editing by Pritha Sarkar)
