Barcelona will now contest in Europe's second tier for the first time in 21 years, finishing third in Group E, leapfrogged at the final moment by Benfica.
West Ham could be travelling to the Nou Camp in the coming months.
Benfica as good as had their work for the night finished, running away with a 2-0 lead in under 25 minutes against group fodder Dynamo Kyiv, leaving everything up to Barca in Munich.
Not long after though, things turned predictably bleak when Robert Lewandowski found space in the away penalty area, and toyed with Gerard Pique before perfectly sending a cross onto Thomas Muller's head.
Muller connected, sending the ball arching over German international teammate Marc-Andre ter Stegen, and saw it cross the line despite a last-gasp clearance from Ronald Araujo.
The goal marked Muller's eighth in just seven games against Barca, and if they hadn't had enough of a reminder of how far they'd fallen, Leroy Sane was there to give new manager Xavi another.
His strike just before the break was reminiscent of the kind of magic Barca wingers of the past would produce, finding its way through ter Stegen's fingertips to end the tie.
Jamal Musiala added some gloss in the second period with another goal, but Bayern's 18 points from 18 could hardly contend with Barca's headline-making collapse into the Europa League.