Despite the absence of injured star forwards Vivianne Miedema and Beth Mead, the Gunners blew Bayern away in the first half.
Frida Maanum levelled the tie with a blistering strike in off the underside of the crossbar on 20 minutes.
Moments later Arsenal led as Stina Blackstenius had the simple task of rounding off a brilliant team move with a header into an unguarded goal from Katie McCabe's cross.
Only some wasteful finishing from Jonas Eidevall's side meant there was a nervy finale.
Leah Williamson and Caitlin Foord missed glorious chances to extend the lead, while Lotte Wubben-Moy hit the crossbar.
But Arsenal held out to extend Bayern's wait to win the competition.
Chelsea hold the upper hand ahead of Thursday's blockbuster quarter-final clash after the English champions won 1-0 away to Lyon in the first leg.
Wolfsburg also hold a 1-0 lead in the other quarter-final over Paris Saint-Germain ahead of the second leg in Germany.
