GLASGOW, Scotland (AP) Thomas Mueller led Germany to a 3-2 away win over Scotland on Monday as the world champions took a big step toward European Championship qualification.
Mueller opened the scoring in the 18th minute and claimed his second in the 34th, six minutes after Scotland had equalized through Mats Hummels' own goal.
James McArthur pulled Scotland level for a second time two minutes before the break, but Mueller and Ilkay Gundogan exchanged passes for the latter to claim Germany's winner in the 54th.
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With two games remaining, Germany is assured of at least a playoff place and needs just one more point to assure qualification.
Also in Group D, second-place Poland routed Gibraltar 8-1 at home, while Ireland consolidated third place and boosted its hopes of a playoff with a 1-0 win over Georgia in Dublin.
The top two qualify for Euro 2016 in France, as does the best third-placed team from all the groups, while the other eight third-placed finishers enter the playoffs.
Mueller now has five goals in three Bundesliga games for Bayern Munich and three goals in two qualifiers for Germany since the season began.
''It's going well at the moment. I feel good, the ball is falling in the right place and I'm making the right decisions,'' said Mueller, who has scored 13 goals and set up three more in 16 games for Germany since the start of the World Cup last year.
The attacking midfielder broke the deadlock by running at the Scottish defense and firing a shot that was deflected before rolling inside the right post.
Scotland equalized when Manuel Neuer saved Shaun Maloney's free kick only for the ball to rebound off Hummels' chest and in.
Emre Can gave the free kick needlessly away, though he atoned with his involvement in Mueller's second goal.
Scotland goalkeeper David Marshall could only parry the unmarked Can's shot and Mueller was well-placed to head in the rebound.
''Thomas has a run and he's where a forward has to be. He has a nose for such situations,'' Germany coach Joachim Loew said.
Neuer was beaten for a second time when McArthur lashed in a thumping shot after the German defense could only half-clear a corner.
But Mueller stepped up again, producing an intelligent off-the-ball run for Gundogan to play him through and then returning the favor for the Borussia Dortmund midfielder to score via the post.
''He set it up so well there was nothing for me to do but shoot the ball into the goal,'' Gundogan said.
In Warsaw, Kamil Grosicki, Robert Lewandowski and Arkadiusz Milik all scored twice, Jakub Blaszczykowski converted a penalty and substitute Bartosz Kapustka netted late for Poland, before Jake Gosling claimed an 87th-minute consolation for Gibraltar.
John Walters' 69th-minute goal was enough for Ireland, which looked short of inspiration until Jeff Hendrick cut open the Georgian defense.
Hendrick eluded two defenders on the edge of the penalty area, then skipped past another challenge and squared the ball for Walters to prod home from close range.
Ireland, which next plays Germany at home then Poland away, has a five-point lead over Scotland, which plays Poland at home then Gibraltar away.