The dismissal made a daunting task become even more difficult for the visitors who went further behind on 65 minutes when Thiago Alcantara side-footed a second from a cross by Joshua Kimmich.
Niklas Suele had another effort disallowed for a foul before Kimmich rounded off the night by waltzing round the keeper to roll the ball into an empty net for Bayern's third.
(Reporting by Neil Robinson; Editing by Toby Davis)
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