Phillip Lahm gave Bayern the lead early on and Mario Mandzukic netted a late second for the German side.
Gerardo Martino has just been appointed coach of Barcelona, for whom Neymar, Xavi and Andres Iniesta were absent.
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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.