Fenerbahce were awarded the penalty after a VAR review but Gokhan Akkan saved Caner Erkin's penalty kick in the 32nd minute.
The half time ended 0-0 at the Caykur Didi Stadium. In the second half, Caykur Rizespor's Milan Skoda scored a powerful header in the 59th minute to give his team a 1-0 lead.
This goal was also recorded as the first goal of the new season in the league. Gokhan Gonul equalized the game with a header in the 76th minute.
In the 87th minute, the away team were given a penalty again and Jose Sosa converted the penalty to seal a comeback victory for Fenerbahce.
Week 1 fixtures of the Super Lig are as follows:
Saturday:
Demir Grup Sivasspor - Aytemiz Alanyaspor
Fatih Karagumruk - Yeni Malatyaspor
Goztepe - Yukatel Denizlispor
Galatasaray - Gaziantep FK
Sunday:
Hes Kablo Kayserispor - Kasimpasa
Trabzonspor - Besiktas
Fraport TAV Antalyaspor - Genclerbirligi
MKE Ankaragucu - Buyuksehir Belediye Erzurumspor
Monday:
Hatayspor - Medipol Basaksehir