Cameroonian forward Vincent Aboubakar opened the scoring for Besiktas in minute 44 with the only first-half goal at Ataturk Olympic Stadium.
Ghanaian midfielder Bernard Mensah doubled the lead in minute 50 and Canadian forward Cyle Larin scored the third goal in the 66th minute.
Mensah had another goal in minute 70, making it 4-0. Fabio Borini's penalty shot in the 78th minute spoiled the clean sheet for Besiktas.
Besiktas are at top of the Turkish Super Lig standings with 41 points. Fatih Karagumruk are in the eighth spot with 27 points.