Mario Gotze scored twice to help Germany take over the top spot in European Championship qualifying Group D with a 3-1 win over Poland on Tuesday.
Germany opened the scoring after 12 minutes when Jonas Hector was played through and cut back for Muller to tap home from six yards.
In the 19th minute, Gotze cut inside and fired Germany's second past Lukasz Fabianski.
Robert Lewandowski became the third Bayern Munich player to score on the day when he got one back for Poland in the 37th minute.
Poland forced Germany keeper Manuel Neuer to make some fine saves as they pushed for an equaliser, but Gotze made the lead comfortable in the 82nd minute with the simplest of tap-ins after Fabianski could only parry a deflected shot directly into his path.
The World Cup champions got a measure of revenge on their eastern neighbours after losing the reverse fixture last October 2-0 in Poland's first win over Germany in 19 tries.
Poland are two points back in second place and two ahead of Republic of Ireland, who defeated minnows Gibraltar 4-0.
Cyrus Christie scored in the first half before Robbie Keane added two after the break and Shane Long added a fourth to boost Ireland's chances of at least reaching the qualification playoffs by finishing third.
Scotland's hopes for the same took a major dent as they lost away to Georgia 1-0 earlier in the day.
The visitors had some bright early spells but failed to trouble the home goalkeeper and Georgia improved before Valeri Kazaishvili fired them in front in the 37th minute.
Scotland struggled to carve chances and Georgia stood firm to a succession of late crosses and corners.
Northern Ireland sensationally went top in Group F as they won 3-1 at the Faroe Islands.
Gareth McAuley's 12th-minute opener was cancelled out by Joan Simun Edmundsson in the 36th, but Edmundsson's second yellow card in the 65th minute opened things up for the visitors.
McAuley scored his second goal six minutes later and Kyle Lafferty soon added a third goal to put Northern Ireland on 16 points, one point clear at the top of their group with three games to play.
Romania fell to second in the group after failing to break down third-placed Hungary in a goalless draw.
Hungary are four points behind Northern Ireland ahead of their showdown in Belfast on Monday.
Greece's disastrous qualifying campaign continued with a 1-0 loss at home to Finland, Joel Pohjanpalo's 75th-minute goal the difference.
The winless Greeks stayed bottom of the table on three points and were officially eliminated from qualifying.
Denmark and Albania both missed a chance to separate themselves in Group I, as a 0-0 draw kept them even on 11 points, one behind leaders Portugal.
Sokol Cikalleshi's header in the 23rd minute almost put the visitors ahead but Denmark dominated the second half with attempts by Nicolai Jorgensen, Nicklas Bendtner and Daniel Agger.
A goal after the break by Bendtner was adjudged to be offside, while the visitors surprised the Danes with more offensive play than expected.
Serbia, who were docked three points for their abandoned home match last October, finally won their first game of the campaign, 2-0 over Armenia to get back on positive points in Group I.
An own goal from Levon Hayrapetyan put Serbia head and Adem Ljajic doubled the lead nine minutes into the second half.