Visitors' Egyptian forward Mostafa Mohamed drew the first blood in the Black Sea province of Rize, scoring a left-footed strike in the area in minute five.
The home team led the first half 2-1.
In the 75th minute, Galatasaray equalized as Mohamed had an easy chance to make a close-range finish thanks to decent teamwork.
After Mohamed's goal, Rizespor's prolific forward Pohjanpalo headed the ball as he was on the goal line of Galatasaray but his header was parried by Galatasaray goalkeeper Fernando Muslera.
Galatasaray were down to 10 men on the pitch in minute 86 as the Lions' central midfielder Berkan Kutlu fouled Rizespor's Lebogang Phiri with a professional foul in the area, preventing him from scoring.
Rizespor were awarded a penalty kick and Kutlu was shown a red card.
In the 87th minute, Rizespor winger Fernando Boldrin missed the penalty sending the ball wide, the game's turning point.
Rizespor took risks and pressured their 10-man opponents.
However, on a quick counter-attack after a corner, Galatasaray's Morutan scored the winning goal in the 101st minute to name the result 3-2 for his team.
Lions forward Mbaye Diagne controlled the ball and then exchanged passes with his teammate Kerem Akturkoglu. Diagne persisted to dribble past two Rizespor players over physical collisions and entered the area from the right flank to find Morutan in the far post.
The Romanian midfielder was unmarked to score an open goal.
Morutan's winner was checked for a possible foul but the referee said it was valid.
Rizespor players argued with the referee as the home team claimed that Diagne fouled before his assist.
Fenerbahce top Super Lig over home win
Meanwhile in Istanbul, leaders Fenerbahce beat Kasimpasa 2-1 earlier Sunday at their home ground Ulker Stadium.
German forward Mergim Berisha scored for Fenerbahce to make it 1-0 in the 16th minute.
In the first half's injury time, Fenerbahce's Brazilian midfielder Luiz Gustavo scored a classy goal, firing a low shot outside the box as the Yellow Canaries led the first half 2-0.
Kasimpasa's Michal Travnik scored a second-half goal in the Fenerbahce area with a left-footed strike to narrow the gap but Fenerbahce secured the 2-1 victory to be on top of the league with 19 points.
Week 8 results
Fraport TAV Antalyaspor - Adana Demirspor: 1-2
VavaCars Fatih Karagumruk - Medipol Basaksehir: 3-1
Ittifak Holding Konyaspor - Aytemiz Alanyaspor: 1-1
Yukatel Kayserispor - Trabzonspor: 1-2
Goztepe - GZT Giresunspor: 0-1
Besiktas - Demir Grup Sivasspor: 2-1
Oznur Kablo Yeni Malatyaspor - Atakas Hatayspor: 0-2
Fenerbahce - Kasimpasa: 2-1
Gaziantep - Altay: 4-1
Caykur Rizespor - Galatasaray: 2-3
|6.ITTIFAK HOLDING KONYASPOR||8||3||5||0||12||8||4||14|
|7.VAVACARS FATIH KARAGUMRUK||8||4||2||2||14||11||3||14|
|13.DEMIR GRUP SIVASSPOR||8||2||3||3||11||9||2||9|
|14.FRAPORT TAV ANTALYASPOR||8||2||2||4||8||12||-4||8|
|17.OZNUR KABLO YENI MALATYASPOR||8||2||0||6||7||16||-9||6|