Polish-born Podolski scored on both sides of the interval to hand Germany first place in the group with three points, leading Croatia who beat Austria 1-0 earlier on Sunday on goal difference.
Germany keeper Jens Lehmann showed some instability at the start of the game when he rammed into defender Per Mertesacker and fumbled the ball into the path of Jacek Krzynowek who fired over the bar after only forty seconds.
But it was all Germany from there on as the three-times European champions launched raid after raid against Polish keeper Artur Boruc.
It started with Miroslav Klose escaping the offside trap to go one on one with Boruc, but selflessly squared the ball to the onrushing Mario Gomez who slides and nudges the ball astonishingly wide in the fourth minute.
Klose, who is also of Polish descent, was more successful on his second attempt. The Bayern Munich ace broke free and set up the unmarked Podolski who slotted home with ease in the 20th minute.
Germany continued to dominate all aspects of the game in the first half but Poland's players seemed rejuvenated.
It took Germany sometime to regain their composure and secured the win in the 72 minute when Podolski volleyed home.
Germany next take on Croatia while Poland play co-hosts Austria on Thursday.