Bayern now have four wins from four, but this victory, against one of their closest rivals, was particularly impressive.
Toni Kroos and Thomas Mueller got the goals for Bayern, who now have a five point advantage over champions Borussia Dortmund, who surprisingly lost 3-2 at struggling Hamburg.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.