Match ends, Germany 3, Poland 1.
Germany moved to the top of Euro 2016 qualifying Group D with a battling victory over Poland.
Thomas Muller put the world champions ahead with a simple tap-in following a sublime move.
Mario Gotze doubled the lead with a terrific individual goal, but Robert Lewandowski's eighth goal of the campaign gave Poland hope.
However Gotze's second - following in after Muller's deflected shot was saved by Lukasz Fabianski - ensured the win.
It gives Germany revenge for last year's 2-0 defeat in Poland and puts them in a strong position with just three games remaining.
At times during this qualifying campaign, Germany have failed to live up to their world champions billing, but in Frankfurt they took charge of the game from the early stages, carving the Poles open with some sharp, precise passing - most notably for the opening goal.
Even when Karim Bellarabi was replaced by Ilkay Guendogan and Mesut Ozil was pushed out to the left, the fluidity remained.
All this came against a very good Poland team who, through Lewandowski and Krzysztof Maczynski, forced Manuel Neuer into two world-class saves.
What it means for Scotland and the Republic
There is no question that Germany and Poland are the two best teams in the group.
Scotland did brilliantly to come away with a deserved point from Warsaw and the Republic of Ireland did likewise in Germany.
But this pair are technically better and physically stronger than both Gordon Strachan's and Martin O'Neill's squads.
It will take a monumental effort for either of them to prevent the top two now being the top two at the end of qualifying, meaning the Scots and the Irish are most likely battling it out for third.
Scotland must find a performance of guts, steel and skill to take anything from Germany on Monday.
- 7SchweinsteigerBooked at 79mins
- 18KroosBooked at 61mins
- 16BellarabiSubstituted forGündoganat 53'minutes
- 19GötzeSubstituted forPodolskiat 90+1'minutes
- 22ter Stegen
- 20PiszczekSubstituted forOlkowskiat 43'minutes
- 13RybusBooked at 8mins
- 11GrosickiBooked at 66minsSubstituted forPeszkoat 83'minutes
- 5MaczynskiSubstituted forBlaszczykowskiat 63'minutes
- Nicola Rizzoli
- Shots on Target
Second Half ends, Germany 3, Poland 1.
Attempt missed. Maciej Rybus (Poland) left footed shot from outside the box is close, but misses to the right. Assisted by Jakub Blaszczykowski.
Attempt saved. Tomasz Jodlowiec (Poland) left footed shot from outside the box is saved in the centre of the goal. Assisted by Grzegorz Krychowiak.
Attempt missed. Mesut Özil (Germany) left footed shot from outside the box misses to the left.
Substitution, Germany. Lukas Podolski replaces Mario Götze.
Corner, Germany. Conceded by Lukasz Szukala.
Corner, Germany. Conceded by Lukasz Fabianski.
Attempt saved. Ilkay Gündogan (Germany) right footed shot from the right side of the box is saved in the top left corner. Assisted by Emre Can.
Substitution, Poland. Slawomir Peszko replaces Kamil Grosicki.
Goal! Germany 3, Poland 1. Mario Götze (Germany) left footed shot from the centre of the box to the bottom right corner.
Attempt saved. Thomas Müller (Germany) right footed shot from outside the box is saved in the centre of the goal. Assisted by Mario Götze.
Thomas Müller (Germany) wins a free kick in the attacking half.
Foul by Maciej Rybus (Poland).
Offside, Poland. Arkadiusz Milik tries a through ball, but Robert Lewandowski is caught offside.
Bastian Schweinsteiger (Germany) is shown the yellow card for a bad foul.
Foul by Bastian Schweinsteiger (Germany).
Jakub Blaszczykowski (Poland) wins a free kick in the attacking half.
Attempt blocked. Mario Götze (Germany) right footed shot from the centre of the box is blocked. Assisted by Ilkay Gündogan.
Toni Kroos (Germany) wins a free kick in the attacking half.