In the minute 30 at Nef Stadium, Galatasaray winger Kerem Akturkoglu was fouled in the box. The Lions were awarded a penalty kick after a video assistant referee (VAR) check.
Romanian midfielder Alexandru Cicaldau scored from white spot to give Galatasaray a 1-0 lead in the first half.
In the early minutes of the second half, the shots of Trabzonspor's Danish forward Andreas Cornelius and Turkish defender Ahmetcan Kaplan shaved the post each.
Trabzonspor leveled the match as Greek midfielder Anastasios Bakasetas scored in the 84th minute.
Galatasaray's Brazilian defender Marcao was unable to clear the danger after Trabzonspor right back Bruno Peres' cross.
The ball was on the loose as Bakasetas fired a low shot in the area to beat Galatasaray goalkeeper Fatih Ozturk.
Six minutes later Trabzonspor completed the comeback against the hosts.
The Black Sea club's recent signing, Bosnian winger Edin Visca, has intercepted Galatasaray midfielder Taylan Antalyali's careless pass near the Istanbul team's penalty box and scored the winning goal for Trabzonspor.
Former Medipol Basaksehir player Visca scored his first goal for Trabzonspor.
In the stoppage time, Galatasaray forward Ryan Babel header's near the six-yard-box was parried by Trabzonspor goalkeeper Ugurcan Cakir.
Big individual mistakes in the last minutes cost the earth for Galatasaray as Trabzonspor secured the away victory that shocked the Lions.
Trabzonspor are on top of the standings with 54 points in 23 league matches.
Ittifak Holding Konyaspor, their nearest opponents in standings, have 45 points after a 1-0 win against Altay in the western Izmir province.
Galatasaray are in a horrible season in the Super Lig and now they feel the heat of the relegation zone.
The Lions, who lost four Super Lig matches in a row, come 15th with 27 points.
Sunday's results:
Kasimpasa-Yukatel Kayserispor: 3-1
Atakas Hatayspor-Caykur Rizespor: 0-0
Altay-Ittifak Holding Konyaspor: 0-1
GZT Giresunspor-Aytemiz Alanyaspor: 1-3
Fraport TAV Antalyaspor-Gaziantep FK: 0-0
Galatasaray-Trabzonspor: 1-2
