Lyon clinched an unbelievable victory in the fifth minute of added time when Fekir capped a fine individual performance by netting a 25-yard free-kick.
The home captain ended Saturday's (AEDT) thrilling match with two goals and an assist, as his late winner handed Monaco's hopes of defending its title another significant early blow.
Prior to the late drama, it looked like as if all the scoring had been done in the first half at Parc OL.
Mariano Diaz broke the deadlock by netting for a third consecutive league game after the host had twice hit the post early on.
Rony Lopes hit back for Monaco, which was playing without Radamel Falcao after his exploits for Colombia in the international break, but Fekir put Lyon back in front.
Monaco responded again, though, with Adama Traore marking his first appearance of the season in style with a wonderful strike.
Both sides had chances to win it in the second half, but just as it looked like they would have to be happy with a draw ahead of their respective European commitments next week, Fekir settled the match with his seventh top-flight goal of the season.