It was Poland's first defeat in seven Euro 2016 qualifiers with the world champions gaining revenge for losing 2-0 in Warsaw last October to knock Adam Nawalka's side from top of Group D.
Georgia's 1-0 home win over Scotland, who Germany play in Glasgow on Monday, and the Republic of Ireland's 4-0 thumping of Gibraltar means Germany are top with 16 points with Poland second on 14 while Ireland go third with 12, one ahead of the Scots.
"Overall I can only be very satisfied, we produced some super football in the first 35 minutes. The Polish chances came uniquely from our mistakes."
All four goals came from Bayern Munich players as Thomas Mueller gave Germany an early lead, then Goetze made it 2-0 before Poland captain Robert Lewandowski pulled one back with a diving header for 2-1 at the break. Mueller and Goetze then combined for Germany's third on 82 minutes.
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A double from captain Robbie Keane, which took his international tally to 67, and goals from Cyrus Christie and Shane Long saw the Republic of Ireland past Gibraltar in Faro. Martin O'Neill's side next play Georgia in Dublin on Monday.
In Group F, Northern Ireland are just one victory away from their first European championship final as they sit top with 16 points, one point ahead of Romania who were held to a goalless draw in Hungary.
Two goals from Gareth McAuley and a third from Kyle Lafferty sealed the victory with the Faroe Islands hit by Joan Edmundsson's sending off of after 64 minutes for a second bookable offence.
The Northern Irish will qualify if they beat Hungary on Monday night at Windsor Park.
Finland came away with a 1-0 win from Greece in a match between two teams struggling in Group F.