The Nigeria international opened scoring for Okan Buruk’s side after 12 minutes.
Osimhen has now registered nine goals and three assists in eight league appearances for the Yellow and Reds this season.
The 27-year-old was replaced by Deniz Gul one minute after the hour mark.
Yunus Akgün, Aleksey Batrakov, and Rafael Leão scored the other goals for Galatasaray.
Konyaspor fielded Nigerian defender Chidozie Awaziem for the entire duration of the game.
Galatasaray will now shift attention to their UEFA Champions League clash against VfB Stuttgart next Tuesday.
