Trailing 1-0 from the first leg in Germany last week, first-half goals from Frida Maanum and Stina Blackstenius were just reward for Arsenal's ebullient display, as a 2-0 victory at the Emirates turned the tie on its head.
Questionable officiating left Gooners irate during their team's Allianz Arena defeat last week, and similar gripes reared their ugly heads early on when Kim Little was scythed down on the break by Sarah Zadrazil, who got away unpunished.
The challenge left Little unable to continue - Lotte Wubben-Moy came on in her place with 11 minutes gone - as captain Leah Williamson filled the void in the heart of the midfield.
However, there was quite the silver lining to that cloud, as Williamson was involved in a deserved opener for Jonas Eidevall's side with 19 minutes gone, as Arsenal suffocated Bayern with their intense pressing and got their reward.
After forcing Bayern into giving the ball away, a sublime one-touch passing move involving Lia Walti, Blackstenius and Williamson ended with the latter laying off Maanum with a cheeky flick, and the Norwegian picked out the top corner with an outstanding long-range strike off the crossbar.
Level on aggregate, Arsenal were not resting on their laurels on a rain-soaked North London night, and they doubled their advantage on the 26-minute mark, as Katie McCabe's cross evaded Saki Kumagai, and Blackstenius could not miss with a header from a couple of yards out.
A rampant Arsenal could have been out of sight just before half time, as Wubben-Moy's dangerous cross-cum-shot had Maria Grohs scrambling, but the ball struck the crossbar as Bayern survived.
The Germans inevitably began to up the ante in the second half, but Manuela Zinsberger's clean sheet remained intact, largely thanks to a crucial Wubben-Moy block from Lina Magull in the 60th minute.
Caitlin Foord wasted another gilt-edged chance to extend Arsenal's advantage in the 73rd minute - leaning back and curling over the crossbar from 12 yards - and McCabe hobbling off in the dying embers was hardly a sight for sore eyes.
Nevertheless, the Gunners survived relentless Bayern pressure and seven minutes of added time to reach the semis for the first time since the 2012-13 season, having suffered three successive quarter-final exits since.
Eidevall's team will now take on either Paris Saint-Germain or Wolfsburg in the final four, with the Germans currently 1-0 up in their quarter-final, while Barcelona thumped Roma 6-1 on aggregate to set up a semi-final showdown with Lyon or Chelsea.