Mame Thiam gave the away side lead in the first half and Enner Valencia doubled the lead eight minutes after the second half started at the Ataturk Olympic Stadium.
Fabio Borini made the score 2-1 by striking a powerful shot but Fatih Karagumruk could not equalize the score in the rest of the game and suffered the first loss after four league games.
Fenerbahce now have 51 points to sit top of the Turkish Super Lig while Fatih Karagumruk are at the eighth spot with 37 points.
Saturday's results in Super Lig:
Hes Kablo Kayserispor - MKE Ankaragucu: 0-0
Trabzonspor - Gaziantep FK: 1-0
Fatih Karagumruk - Fenerbahce: 1-2
