Pierre Webo opened the scoring for last season's runners-up, before Lamine Diarra levelled on the stroke of half-time.
Moussa Sow then snatched all three points for Fener in the dying seconds, extending their lead to six points over second-placed Kasimpasa, who lost ground on the leaders in a 1-1 draw with Bursaspor.
Sebastian Pinto put the hosts ahead at the Bursa Ataturk Stadium on Saturday, but Ezequiel Scarione pulled Kasimpasa level before the break.
The draw leaves Kasimpasa just one point clear of Besiktas, who climbed to third with a convincing 3-1 win against Konyaspor on Monday.
Slaven Bilic's men raced into a 3-0 half-time lead and their opponents could only muster a single goal in reply after the interval.
The three points lifted Besiktas above Galatasaray and Sivasspor, who contested an entertaining encounter two days earlier.
Selcuk Inan scored the winner from the penalty spot for Galatasaray in a 2-1 victory that featured four red cards.
Sivasspor finished with eight men after losing Manuel Da Costa and Cicinho in the closing stages.
At the other end of the table, Kayserispor picked up a shock 2-0 win at Rizespor to move off the bottom of the table.
Elazigspor's 3-1 defeat to fellow strugglers Gaziantepspor saw the former slip to 18th and deeper into the relegation mire.
Elsewhere, Trabzonspor recorded a 1-0 victory over Eskisehirspor to leapfrog their opponents into sixth; Kayseri Erciyesspor stayed out of the relegation zone with a 1-0 win against Genclerbirligi and Akhisar Belediye fell to a 1-0 defeat at home to Karabukspor.
