Miha Zajc opened the score in the 26th minute and the first half ended 1-0 at the Sukru Saracoglu Stadium in Istanbul.
Fenerbahce made it 2-0 with Serdar Dursun's goal in the 68th minute and the match ended 2-0.
Fenerbahce placed are now placed second with 59 points, while Galatasaray lay at the 14th spot with 41 points in the Super Lig standings.
Super Lig results:
Oznur Kablo Yeni Malatyaspor-GZT Giresunspor: 0-1
Demir Grup Sivasspor-Medipol Basaksehir: 0-2
Adana Demirspor-Altay: 3-1
Fenerbahce-Galatasaray: 2-0
