Grenier fired a 30-metre free-kick into the top corner 14 minutes from time to cancel out Dario Cvitanich's opener, shortly after midfielder Maxime Gonalons had been sent off for a second bookable offence.
Lyon have 64 points with one game left and lead fourth-placed Saint-Etienne by two points and fifth-placed Lille by three.
Nice are sixth, level on points with Lille before travelling to AC Ajaccio next Sunday. Lille will take on Saint-Etienne while Lyon will entertain Stade Rennes.
Champions Paris Saint-Germain and second-placed Olympique Marseille have already secured their places in the group stage.
The third-placed team in Ligue 1 play in the Champions League's third qualifying round.
At Nice's Stade du Ray, the sun was back after heavy rain had forced the French League to postpone the game which was initially scheduled to kick off on Saturday with all the other Ligue 1 games.
Bakary Kone brought down Cvitanich in the box early in the second half and the Argentine striker converted the resulting penalty by wrong-footing Anthony Lopes.
Lyon did not give up, however, and twice came close after nice team moves, only for Steed Malbranque to shoot straight at Lopes on both occasions.
Gonalons then picked up two yellow cards in the space of nine minutes and the visitors were heading towards defeat until Grenier's stunning strike.
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