Fenerbahce were reduced to 10 men when Irfan Can Kahveci received a straight red card for a foul on Manolis Siopis after a VAR review in the 18th minute at Ulker Stadium.
Four minutes later, Anthony Nwakaeme scored the opener after rolling into the net with a right-footed shot from inside the box.
Fenerbahce were so close to scoring an equalizer in the 35th minute but Serdar Dursun's header was blocked on the line by Ahmetcan Kaplan.
The same side made the score 1-1 after Miha Zajc found the net with a header off a free kick in the 71st minute.
Near the end of the match, Nwakaeme attempted to score again but his shot from close range hit the post and the match ended in a 1-1 draw.
Third-place Fenerbahce have 47 points.
After collecting 67 points, Trabzonspor are now 15 points clear at the top of Super Lig, ahead of second-place Ittifak Holding Konyaspor.
