Osimhen opened scoring for Lille in the 14th minute after he was set up Jonathan Bamba.
The 21-year-old has now scored 12 goals and recorded four assists in 23 league appearances for Les Dogues this season.
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Osimhen was replaced by Nico Gaitan 10 minutes from time.
Renato Sanches doubled the visitors advantage 15 minutes from time following an assist by substitute Luis Araujo.
Lille maintained fourth spot in the table with 40 points from 24 matches.
Christophe Galtier’s men will host Olympic Marseille in their league game on Sunday, February 16.