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Arsenal were left to rue a host of missed chances as Lea Schuller's header gave Bayern a 1-0 victory in their Champions League quarter-final first leg.
The Gunners twice saw chances cleared off the line, from Stina Blackstenius and Leah Williamson, but could not find a way to breach the hosts' defence at the Allianz Arena and were made to pay.
Bayern top scorer Schuller nodded in her 14th goal of the season shortly before half-time and could have doubled her lead on the stroke of the interval.
Arsenal were worth at least a draw and were inches away from finding one again when Caitlin Foord rattled the Bayern woodwork from distance.
They will now need to beat Bayern in the return leg at the Emirates next week to avoid crashing out in the quarter-finals on their fourth consecutive appearance in the competition.
How Bayern held off Arsenal to take lead
In the well-attended and always imposing Allianz Arena, Arsenal seemed slightly intimidated early on but soon settled after weathering a couple of bright moments for the hosts, and they should have gone ahead when Blackstenius nodded over a free header from six yards.The game seemed in their own hands for much of the opening period, regularly keeping Bayern pegged back inside their own half. Frida Maanum missed another strong opportunity from Blackstenius' square ball, with Maria Grohs blocking her effort from close range.
But when Bayern finally regained their composure and built up some momentum of their own, they made it tell. Schuller rose high above Laura Wienroither to nod into the top corner for the opener. She could have doubled the lead moments before the break, but lifted an effort just wide of the far post after splitting Arsenal's two centre-backs.