Visitors Trabzonspor took the lead in the first half as Swedish winger Erkan Zengin scored from a penalty kick in the 25th minute.
In 59’, Trabzonspor midfielder Ozer Hurmaci was sent off after a sliding tackle against the Lions’ left back Lionel Carole.
Dominant through much of the game, Galatasaray equalized in the 63th minute with their German star, Lukas Podolski. The 30-year-old forward smashed the ball into the net after trapping it in the area.
In 70’, Trabzonspor center back Aykut Demir was brandished his second yellow card by the referee after he argued with Podolski.
Retaining possession of the ball more after Trabzonspor players' exit, Galatasaray pressed more to score the winning goal.
The Lions were awarded a penalty near the end of the game as Umut Bulut was brought down by Trabzonspor defender Cavanda. Turkish midfielder Selcuk Inan converted the penalty successfully in the 89th minute, winning a crucial lead for his team in the clutch.
Achieving a comeback in the nick of time, the Istanbul club won the match 2-1 and ended their three-match poor run in the league.
After the penalty decision, Trabzonspor defenders Cavanda and Salih Dursun were both shown red cards.
In the heat of the moment, Turkish right-back Dursun took referee's red card and brandished him the red card to protest his decisions, and was sent off as a result.
Galatasaray stars Podolski and Wesley Sneijder will miss the upcoming league match against Gaziantepspor after collecting their fourth yellow cards each.
Galatasaray climbed to the third spot with 37 points, while Trabzonspor are in the ninth position with 27.
Meanwhile, league leaders Fenerbahce drew against Bursaspor 0-0 on Saturday. The Yellow Canaries raised their points to 50.
Super Lig title contenders Besiktas will meet Genclerbirligi at home on Monday.
Genclerbirligi has had an excellent run in the league, winning their last four matches.
Besiktas center-back Rhodolfo sustained a major ligament injury in his knee, keeping him out until early July.
The match at Basaksehir Fatih Terim Stadium will begin at 8 p.m. local time in Turkey [1800GMT].
In second place with 48 points, Besiktas will take the lead if they win against Ankara-based Genclerbirligi.
The Black Eagles will still have a match to play -- after a game against Trabzonspor on Jan. 24 was delayed due to weather conditions. It will be played in Trabzon on March 15.