Osimhen scored the decisive goal in the 16th minute after he was set up Jonathan Ikone.
The 20-year-old has now scored nine goals and recorded three assits in 16 league appearances for Les Dogues this season.
The former Sporting Charleroi of Belgium striker is now third on the top scorers chart along with Metz’s Habibou Diallo.
Christophe Galtier’s men moved from fourth to third position in the Ligue 1 table with 28 points from 17 matches following the win.
Lille will now shift attention to Tuesday’s UEFA Champions League away fixture against Chelsea at the Stamford Bridge.