The Black Sea Storm kept their chances of European football alive with the win, moving into fifth place just one point behind fourth placed Başakşehir.
The entertaining game saw a total of 36 shots, three goals and a whopping 15 bookings as well as a red card.
The match was marred by a brawl between the Galatasaray and Trabzonspor players in the last minutes of the game.
Aurelian Chedjou and Mehmet Ekici had an altercation that ended up spiralling out of control.
Both the Galatasaray and Trabzonspor goalkeepers got involved as did a number of players on the sidelines.
The referee ended up booking six players and sending off Özer Hurmacı.
Galatasaray playmaker Wesley Sneijder will not be able to play next weeks league game due to suspension.
The Lions dropped into second place following the loss and could fall into third position if Fenerbahçe beat Bursaspor today.