A strike from Jorge Djaniny gave the visitors a 1-0 advantage going into the second half, with Caleb Ekuban doubling the lead in the 54th minute.
Robert Piris fired in from the penalty spot to make it 2-1 in the 86th minute, but Trabzonspor held on for a narrow win in Ankara. Trabzonspor are now fifth in the league with 33 points, while Genclerbirligi sit at 18th spot with 19 points.