The reigning champions won their first game under the stewardship of recently appointed manager Mustafa Denizli who replaced Hamza Hamzaoğlu a fortnight ago.
Yasin Öztekin doubled the score on 80 minutes and Podolski setup Burak Yılmaz with the third and final goal just before the final whistle.
Podolski now has a total eight goals and two assists in all competitions for the Lions this season.
Galatasaray 3-0 Bursaspor
Kick-Off: 18:00 GMT
Stadium: Türk Telekom Arena
Galatasaray: Muslera, Sabri, Chedjou, Semih, Hakan, Selçuk, Jose Rodriguez, Yasin, Sneijder, Podolski, Burak
Subs: Cenk, Olcan, Bilal, Emre, Tarık, Sinan, Umut
Bursaspor: Mert, Erdem, Serdar, Dany, Emre, Aziz, Bekir, Traore, Dzsudzsak, Josue, Necid
Subs: Harun Tekin, Cristobal Jorquera, Isaac Cuenca, Luis Advincula, Hajime Hosagai, Tom De Sutter, Tomas Sivok
Goals: 68′ Podolski, 80′ Yasin, 90′ Burak Yılmaz