The victory sealed a triumphant return to the club for veteran coach Fatih Terim, who took the reins for the fourth time last December.
Basaksehir have risen rapidly over the last two seasons to rival the established Istanbul triumvirate of Besiktas, Fenerbahce and Galatasaray.
64-year-old Fatih Terim, also known as 'emperor', will replace sacked Croatian manager Igor Tudor, the Turkish club said.
The decision comes after Terim was allegedly involved in a brawl with a restaurant owner in a Aegean coastal resort town.
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