Trabzonspor faced a difficult task after being reduced to 10 men in the 20th minute when Okay Yokuslu was sent off for violent conduct.
Onana initially kept Fenerbahce's attacks at bay, but in the 45th minute, he misjudged a tame long-range effort from his former teammate Fred, spilling the ball into the path of Sebastian Szymanski.
The Cameroon international managed to block Szymanski's follow-up, but the rebound fell kindly to Youssef En-Nesyri, who calmly tapped the ball into an open net.
Trabzonspor will face Gaziantep in their upcoming league fixture, which will also mark Onana's home debut at Akyazi Stadium.
