Mahmut Tekdemir found the net to give the away team an early 1-0 lead in the sixth minute at Ulker Stadium.
But Nazim Sangare equalized the match in first-half stoppage time. After the break, Marcel Tisserand made it 2-1 for Fenerbahce as Basaksehir were down to nine men after Rafael and Irfan Can Kahveci were sent off.
The match opened up after that and Fenerbahce secured the win after Luiz Gustavo and Mert Hakan Yandas' goals against a nine-man squad.
Basaksehir manager Okan Buruk was also forced to leave the field after receiving a red card in minute 71.
After losing two consecutive league matches, Fenerbahce gained a remarkable win to increase their point total to 26. Basaksehir's winless streak in the league has reached five with the defeat and the team has 15 points.
Wednesday's results in Super Lig:
Buyuksehir Belediye Erzurumspor - Yukatel Denizlispor: 1-2
Aytemiz Alanyaspor - Yeni Malatya: 1-1
Kasimpasa - Gaziantep FK: 0-4
Fenerbahce - Medipol Basaksehir: 4-1
