Serge Gnabry all but rubber-stamped Bayern's place in the last eight with a fourth goal before half-time but there was no let-up after the break.
Thomas Muller gleefully helped himself to two goals, either side of Maurits Kjaergaard's excellent consolation, with Leroy Sane thumping in number seven late on - it was a record seventh time the Bavarian outfit had hit seven in a game in the competition.