The Lions drew first blood with Halil Dervisoglu in the 39th minute at Nef Stadium.
Former Galatasaray player Ryan Donk equalized in the 47th minute just before the end of the first half.
Umut Bozok made it 2-1 for Kasimpasa in the 60th minute and Kevin Varga brought the final score to 3-1 in the 93rd minute.
Galatasaray suffered their third straight loss in the Super Lig and manager Domenec Torrent lost his first two matches with the Lions with this defeat.
Galatasaray is 13th in the Super Lig standings with 27 points while Kasimpasa is 17th with 21 points.
Thursday's Results:
Aytemiz Alanyaspor-Atakas Hatayspor: 6-0
Caykur Rizespor-Fraport TAV Antalyaspor: 2-1
Galatasaray-Kasimpasa: 1-3
