Bayern's 3-2 win at Old Trafford, headlined by a double for childhood United fan Pernille Harder, gave the German side the advantage before the second leg, but with 11 minutes gone, Malard Melvine made the most of a Bayern defensive mix-up to give United the lead on the night and level up the tie.
United then held firm despite waves of Bayern pressure. Harder forced a last-ditch save from United goalkeeper Phallon Tullis-Joyce early in the second half.
Germany captain Giulia Gwinn then went close just inside the final quarter-hour. The dam finally broke after 81 minutes when Glodis Viggosdottir headed in a rebound from Bayern's 13th corner of the match.
Bayern took just three minutes to score again and put the result beyond doubt, with Dallmann thumping an excellent effort from the edge of the box past Tullis-Joyce and into the top corner.
Bianca Rech, the sporting director of FC Bayern Women, spoke very positively about Pernille Harder after the game. After reaching the Champions League semi-finals, Rech raved: "When you look at Pernille Harder, at her mentality, her quality – she is simply a player who makes the difference in the big games."
The win sends Bayern to the semis for the first time since 2021, where they are likely to take on Spanish champions Barcelona, who beat them 7-1 in the group stage.