Galatasaray scored the opener in the 20th minute as Turkish midfielder Emre Kilinc finished in a one-on-one position at Trabzon's Medical Park Stadium.
Trabzonspor's Edgar failed a back pass to goalkeeper Ugurcan Cakir as Kilinc intercepted the ball to score.
In the 33rd minute, Galatasaray doubled the lead as Kilinc scored again.
Trabzonspor goalkeeper Cakir left his goal to tackle Galatasaray's Kerem Akturkoglu, but Cakir was unable to catch the ball. Halil Dervisoglu made a quick one-touch pass to Kilinc, who was roaming free around the penalty spot to make it 2-0 for the Lions.
Home team Trabzonspor did not give up, as in the 41st minute the Black Sea club's Danish forward Andreas Cornelius scored a close range goal.
Galatasaray led the first half 2-1 but Trabzonspor equalized in the 62nd minute.
Hamsik skipped a Galatasaray defender and passed the ball inside. Nigerian winger Anthony Nwakaeme, who was unmarked in the area, controlled the ball and took his time to score with a right-footed strike, 2-2.
Galatasaray displayed a disappointing performance as the Lions could not secure the lead.
So the match of the week ended as a 2-2 draw as points were shared.
Second-placed Trabzonspor have 10 points in four matches in the Super Lig led by Besiktas, who earned 10 points as well.
Besiktas topped the standings by goal average.
Similar to Besiktas and Trabzonspor, Fenerbahce and Ittifak Holding Konyaspor got 10 points in four games.
Fifth-placed Galatasaray have 8 points to chase the top four in the league table.
VavaCars Fatih Karagumruk - Adana Demirspor: 4-0
Ittifak Holding Konyaspor - Altay: 3-1
Yukatel Kayserispor - Kasimpasa: 2-0
Besiktas - Oznur Kablo Yeni Malatyaspor: 3-0
Caykur Rizespor - Atakas Hatayspor: 0-2
Fenerbahce - Demir Grup Sivasspor: 1-1
Goztepe - Medipol Basaksehir: 2-1
Trabzonspor - Galatasaray: 2-2
Gaziantep - Fraport TAV Antalyaspor
Aytemiz Alanyaspor - GZT Giresunspor