The Lions hosted Gaziantepspor at the Turk Telekom Arena and were a goal down after – minutes when Muhammed Demir found the back of the net.
Podolski struck back immediately for the home side when he headed in a well placed cross from Jason Denayer.
Umut Bulut scored his first goal of the season to give Galatasaray the lead in what turned out to be the winning goal.
The Germany international was an Arsenal player before joining Galatasaray on a three-year transfer over the summer transfer window.
Podolski has three goals for the Istanbul giants and started the game behind striker Umut Bulut.
The reigning Turkish Super League champions are currently 3rd in the league with 11 points after six games.
Galatasaray take on Astana in the UEFA Champions League during the week and Istanbul BB in the league next weekend.