Fenerbahce broke the deadlock when Diego Rossi made a close-range finish in the fifth minute, with an assist by Nazim Sangare at Ulker stadium.
In the 57th minute, Fenerbahce forward Serdar Dursun took a penalty kick but missed. After five minutes, Dursun put the ball into Gaziantep FK's net, bringing the score to 2-0.
The visiting side narrowed the gap to one with Angelo Sagal's goal in the 66th minute. The position was checked by the VAR (Video Assistant Referee).
The Yellow Canaries' third goal came from Slovenian midfielder Miha Zajc in the 82nd minute.
Alexandru Maxim netted a stoppage-time penalty to make the score 3-2 in Istanbul.
Second-place Fenerbahce brought their points up to 68, while 16th-place Gaziantep FK now have 42 points on matchday 35.
In another match on Friday, GZT Giresunspor defeated Adana Demirspor 2-0 with goals from Mehmet Umut Nayir and Serginho at Giresun's Cotanak stadium.
GZT Giresunspor jumped to the number 14 spot, boasting 43 points with three matches left in the Super Lig.
