Ismail Kartal's side have not been top of the table since the opening weekend, but the win at the Ataturk Olympic Stadium sees them climb above Galatasaray.
Emmanuel Emenike opened the scoring after just three minutes of the Istanbul derby, converting Alper Potuk's low cut back beyond goalkeeper Tolga Zengin.
An open clash saw both sides create good chances, but Zengin and his opposite number Volkan Demirel kept the score down, the latter saving brilliantly from a Demba Ba header.
Zengin denied Caner Erkin and Emenike before Olcay Sahan was sent off for two bookable offences two minutes before the break.
Moussa Sow, on as a second-half substitute, secured the win with four minutes to play, firing home from the edge of the penalty area to send Fenerbahce top.
Galatasaray stay level with Fenerbahce at the top, though, after they came from behind to beat Kasimpasa 2-1, Umut Bulut sealing the points in second-half stoppage time.
Akhisar Belediyespor wasted their chance to join the two sides on 16 points as they were held to a 1-1 draw by Trabzonspor, while Bursaspor moved into fifth with a comfortable 3-0 win over Sivasspor.
Three goals in 13 second-half minutes from Josue, Volkan Sen and Fernandao sealed the three points for Senol Gunes' side, while Sivasspor finished the game with 10 men after Burhan Eser's late dismissal.
John Chibuike's third goal of the campaign was enough to give Gaziantepspor a 1-0 win over Mersin Idmanyurdu, but Istanbul Basaksehir were unable to follow last week's win over Galatasaray.
Having won 4-0 in their previous game, Abdullah Avci's side fell to a 1-0 defeat at the hands of Genclerbirligi, Nemanja Tomic's 95th-minute winner securing victory.
Konyaspor lifted themselves away from the bottom three with thanks to a 1-0 victory over Karabukspor, while Balikesirspor rescued a 2-2 draw with Eskisehirspor thanks to Nuno Coelho's late equaliser.
Meanwhile, another late goal saw Kayseri Erciyesspor share the points with 10-man Rizespor, Edinho scrambling home a 90th minute-equaliser in wet conditions.
