The Nigeria international scored twice in the keenly contested encounter to help Galatasaray reclaim top spot in the Turkish Super Lig table.
Osimhen gave the Yellow and Reds the lead in the 29th minute, before doubling their lead one minute before the break.
İrfan Kahveci reduced the deficit for Fenerbahçe two minutes after the hour mark.
The hosts, however, maintained their lead for the remainder of the game.
Osimhen came under criticism for his poor form before scoring for Galatasaray in the UEFA Champions League 4-2 victory over his former club, Lille last week.
The 27-year-old said he is not bothered by social media criticism, and is firmly focused on doing his best for the club.
“There were discussions before the match this week. I love this club. I always say it.
