Besiktas suffered a 3-1 defeat over the weekend, so they entered the midweek clash with the determination of earning all the three points.
The hosts shot into the lead in as early as the 6th minute.
However, Kasimpasa scored two quick goals through Bengali-Fode Koita to turn the scales in their favour, before Kevin-Prince Boateng restored parity after his introduction into the game.
As if it was a day for the substitutes Guven Yelcin registered the match-winner in 90th minute, after coming on.
Boateng has three goals and an assist in 10 games for the Black and Whites.