Andrée Jeglertz’s side earned a share of the spoils after coming from two goals down against the German champions.
City knew we’d been handed a difficult first assignment on our return to Champions League action, and fell behind early on to a clinical Giulia Gwinn finish.
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A deflected Lauren Hemp cross hitting the crossbar aside, we were on the back foot for much of the first half and an unfortunate Kerstin Casparij own goal from a Pernille Harder cross made it two inside 30 minutes.
But City rallied and would halve the deficit on the stroke of half-time when Beth Mead pounced on a loose ball to tap into an empty net.
Bayern again pressed forward after the restart, but the WSL champions were handed the chance to pull level after the hour when Aoba Fujino was brought down in the area.
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Bunny Shaw would see her spot kick saved, but City continued to battle for a route back into the game.
We’d deservedly find it with five to go, when Carlotta Wamser was picked out on the left of the area before finding the bottom corner with a low, curling effort.
Check out the best of the action from our UEFA Women’s Champions League opener via the highlights above...