Lea Schueller's first-half goal gave Bayern Munich a 1-0 win over Arsenal in the first leg of their Women's Champions League quarter-final tie on Tuesday.
Germany forward Schueller scored the only goal of the game six minutes before half-time at the Allianz Arena, rising at the back post to head in a hanging cross from the right by Maximiliane Rall.
Arsenal, though, will feel they should have come away with at least a draw to take back for the second leg in London next week, with Caitlin Foord hitting the woodwork early in the second half.
Japan's Saki Kumagai then made a superb goal-line clearance to deny Stina Blackstenius, and Schueller made a similar intervention to prevent Leah Williamson from equalising.
Arsenal, whose 2007 victory remains the only time an English club has won the competition, are looking to avoid going out to German opposition in the quarter-finals for the second year running after losing to Wolfsburg at this stage last season.
The return leg will be played at the Emirates Stadium next Wednesday, before which Bayern must face Wolfsburg in a meeting of the top two in the German Bundesliga at the weekend.
Wolfsburg, who have reached five Champions League finals in the last decade, winning two, visit Paris Saint-Germain in the first leg of their quarter-final tie on Wednesday, when holders Lyon take on Chelsea.
Tuesday's other game sees Barcelona play Roma in the Italian capital.
Barca won the Champions League in 2021 before losing to Lyon in last season's final.