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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.