Stefano Okaka scored the opener for Medipol Basaksehir in the 16th minute at the Basaksehir Fatih Terim Stadium in Istanbul.
In the second half, Fredrik Gulbrandsen doubled the lead in the 90th minute to claim Medipol Basaksehir's first points of the season.
Having collected 10 points, Fenerbahce suffered their first loss in the Super Lig.
