Sivasspor looked set to record a home victory after Atif Chahechouhe bagged a brace after 55 minutes however Burak Yilmaz reduced the lead to one goal in the 60th minute.
Podolski found the back of the net in his debut league appearance via a well placed header in the 81st to save the Lion’s a point.
The German forward joined the Istanbul based side for £1.75 million earlier this summer following an unsuccessful loan spell with Inter Milan.
Galatasaray take on Osmanlispor next weekend at the Turk Telekom Arena.
Stadium: Sivas 4 Eylül
Referee: Barış Şimşek
Sivasspor: Setkus, Cicinho, Ümit, İbrahim, Erkan Kaş, Burhan, Hakan, Adem, Mehdi, Aatif, Batuhan
Manager: Sergen Yalçın
Galatasaray: Muslera, Telles, Chedjou, Hakan Balta, Sabri, Bilal Kısa, Yasin, Selçuk, Olcan, Sneijder, Podolski,
Manager: Hamza Hamzaoğlu