Bertolacci scored another for Karagumruk in the 30th minute before Jure Balkovec made it 3-0 in the 37th minute.
The only goal for Medipol Basaksehir came from Danijel Aleksic in the 84th minute.
After the match, Basaksehir manager Aykut Kocaman announced he would submit his resignation.
Kocaman's team has two wins and six defeats in eight matches in the 2021-2022 season.
Balotelli scores fourth goal in four games as Adana Demirspor win
Fenerbahce is in the top spot in Week 8 of the Turkish Super Lig with 16 points in the table. Adana Demirspor is ninth with 12 points and Basaksehir is fifteenth with 6 points.