The defending champions were made to work hard for the points in an eventful contest, with Michal Kadlec putting through his own net to hand Rizespor the lead, only for the defender to level matters before the interval - those goals sandwiching Dirk Kuyt's penalty miss.
Fenerbahce's cause was aided by Kivanc Karakas' second-half dismissal, with substitute Pierre Webo making the numerical advantage count 10 minutes from time.
Rivals Galatasaray remain level on 19 points with Fenerbahce also due to the contribution of a substitute.
Umut Bulut took four minutes to register the winning goal with a 71st-minute strike as Cesare Prandelli's side won 2-1 at Karabukspor.
Prandelli's men took the lead after two minutes thanks to Aurelien Chedjou, but were pegged back by Emre Gungor in the second half.
Bulut's decisive contribution helped Galatasaray bounce back from their UEFA Champions League humbling at Borussia Dortmund.
Besiktas became the third of the big three to record a come-from-behind 2-1 win after their trip to Istanbul Basaksehir.
Slaven Bilic's side fell behind three minutes from the break but goals from Demba Ba and Kerim Frei in the second half were enough for the win in a fiery affair that saw Besiktas finish with nine men.
Surprise package Mersin Idmanyurdu are fourth thanks to a 2-1 triumph over Balikesirspor, while Gaziantepspor kept the league's top scorer, Theofanis Gekas, quiet and won for the third time in four outings as Muhammet Demir's solitary goal was enough to defeat Akhisar Belediyespor 1-0.
Oscar Cardozo scored two as Trabzonspor recorded their second win of the campaign with a 3-2 victory over Konyaspor, and Shota Arveladze's Kasimpasa fought back twice to earn a 2-2 draw with Genclerbirligi.
The weekend's other two games both ended 1-1, as Sivasspor and Eskisehirspor, along with Kayseri Erciyesspor and Bursaspor could not be separated.
