The visiting team Fenerbahce's Greek midfielder Dimitris Pelkas broke the deadlock in the 76th minute.
In the 83rd minute, Trabzonspor forward Jorge Djaniny's header in the area hit the goalpost and went out. The Yellow Canaries clinched the 1-0 win in Trabzon, a crucial victory that will keep them in the title race.
Fenerbahce are now in the third spot with 54 points, ahead of Trabzonspor which have 48 points. Leaders Galatasaray have 57 points, while second-placed Besiktas have 54 points.
Two Fenerbahce players, midfielder Mert Hakan Yandas and central defender Serdar Aziz, were shown yellow cards to be suspended for the next match. In the upcoming fixture, Fenerbahce will take on Fraport TAV Antalyaspor in Istanbul on Thursday.
Goztepe - Kasimpasa: 1-0
Trabzonspor - Fenerbahce: 0-1