Kerem Aktürkoğlu gave a 1-0 lead to the Lions in the ninth minute but Isaac Thelin scored an equalizer for the away side in the 51st minute.
Galatasaray secured a hard-fought win after Mostafa Mohamed converted the penalty in the 89th minute.
The Lions remain on top of the Super Lig with 51 points by winning six matches in a row, while Kasımpaşa are in the 15th spot with 26 points.
Feb. 14’s results in Süper Lig:
İttifak Holding Konyaspor – Yukatel Denizlispor: 2-0
Atakas Hatayspor – Aytemiz Alanyaspor: 0-0
Göztepe – Medipol Başakşehir: 2-1
Galatasaray – Kasımpaşa 2-1