- Joachim Löw's men go top of Group A, with Poland two points back in second
- Two goals in eight minutes from Thomas Müller and Mario Götze make difference
- Robert Lewandowski replies eight minutes before interval
- Götze clinches victory from close range late on
- Next games: Scotland v Germany, Poland v Gibraltar (7 September)
Germany inflicted Poland's first defeat of UEFA EURO 2016 qualifying as the lead changed hands in Group D, early strikes from Thomas Müller and Mario Götze giving them the decisive advantage in this top-of-the-table contest in Frankfurt.
Joachim Löw's world champions made the group pacesetters pay for their slow start and within 12 minutes were on their way to avenging last October's 2-0 loss in Warsaw and leapfrogging Adam Nawalka's team as leaders. Robert Lewandowski's fine 37th-minute goal better typified the overall Polish display but despite chances of an equaliser Götze sealed the result eight minutes from time.
The early breakthrough followed a sequence of crossfield passes as Jonas Hector, overlapping down Germany's left, played a one-two with Karim Bellarabi and centred to Müller for a tap-in. Poland's three-game unbeaten run against their neighbours was in critical danger come the 19th minute.
Götze cut into the area from the left and let fly a shot that beat Łukasz Fabiański at his right-hand post. Fabiański did deny Müller a potential third and moments later the Poles were back in it with a fine breakaway strike. Captain Lewandowski applied the bullet-header finish that Grosicki's left-wing cross with the outside of the boot deserved.
Germany's Mario Götze celebrates one of his two goals
On the cusp of half-time Poland, hitherto unbeaten, almost restored parity but Neuer tipped over Lewandowski's blistering effort and Götze cleared the No9's header off the line. Götze was the next to be unlucky, however, clipping the post when clear near the hour-mark.
Grzegorz Krychowiak also intervened crucially with blocks from Bellarabi and İlkay Gündoğan. A reminder of the Polish threat came with Neuer's stop from Krzysztof Mączyński's thumping drive.
Grosicki also tested the keeper from a Poland counterattack although Fabiański was back in action to repel Müller and then Mats Hummels, while Kamil Glik threw himself in the way of Götze's strike. There would be no reprieve in the 82nd minute, though, Götze prodding in Germany's third following Fabiański's save from Müller.