The Germans were left heartbroken again after losing the final to the Italians last year whose three away goals tonight enabled them to qualify for the next stage.
Bayern took a 1-0 lead into their home tie but that was soon canceled out when Samuel Eto'o struck for the visitors, however, the Munich faithful were soon sitting comfortably when Mario Gomez and then Thomas Muller made it 2-1 prior to half-time.
Wesley Sneijder gave the Nerazzurri hope just after the hour-mark before Goran Pandev grabbed the third and winning goal for Leonardo's men as last season's runners-up bow out in pure frustration.
Uefa Champions LeagueBayern Munich (GER): 2 (Mario Gomez 21', Thomas Muller 31') Inter Milan (ITA): 3 (Samuel Eto'o 4', Wesley Sneijder 63', Goran Pandev 87') *Inter win on away goals after two-legged tie ended 3-3
Venue: Allianz Arena, Munich Crowd: 69,000 Referee: Pedro Proenca (POR) Yellow cards:BAY - Luiz Gustavo 37', Breno 57' INT - Lucio 59', Goran Pandev 89', Thiago Motta 90', Houssine Kharja 90+2'
GOAL Inter went into the tie a goal down but soon managed to restore parity with a vital away goal in just the third minute when Samuel Eto'o received a through ball from Goran Pandev and despite looking slightly off-side, play was called on and he slotted home in between Thomas Kraft's legs to join Lionel Messi on eight goals for the tournament.
GOAL Bayern replied in the 21st minute to repair their overall lead when Arjen Robben whipped a shot at Julio Cesar from outside the area, forcing the Brazilian to spill the ball, where it fell close to Mario Gomez who flicked it over his head and Inter defender Maicon was unable to clear it off the line as the Allianz Arena fans erupted.
GOAL Louis van Gaal's men then netted their third goal of the two-legged tie, and their second for tonight's match, on the half-hour mark when Thomas Muller managed to produce a sublime finish. Robben had played a ball into the path of the Germany international and although it took a deflection off an Inter defender, Muller controlled before finishing neatly with the outside of his right boot to make it 2-1 (3-1 on aggregate).
The home side should have been further ahead with about five minutes remaining in the opening half when Gomez used his determination to chase a ball down to the byline before flicking back across goal only to see the ball dribble along the goal-line where Inter defender Andrea Ranocchia cleared onto the boot of Muller and off the upright in a bizarre incident just prior to half-time.
GOAL Inter were determined to get back into the match and that moment occurred in the 63rd minute when Wesley Sneijder, who had a few earlier half-chances, received a lovely little cushioned ball from Eto'o on the edge of the area and the Dutchman hammered home past Kraft to give his side plenty of hope with one more goal sending them through to the next phase.
Both sides were chasing goals in a very open affair with Bayern trying to kill off the tie and the reigning champs hoping to keep themselves alive and it was the latter which occurred with three minutes of regular time remaining.
GOAL Eto'o was again the architect, beating off competition from Breno before teeing it up for Pandev who fired home into the roof of the net to somehow move through to the quarter-finals after being seemingly down and out at half-time.
Bayern Thomas Kraft (gk), Philipp Lahm, Daniel van Buyten (Badstuber 70'), Breno (Kroos 90'), Arjen Robben (Altintop 67'), Bastian Schweinsteiger, Franck Ribery, Danijel Pranjic, Luiz Gustavo, Mario Gomez, Thomas Muller
Subs - Hans-Jorg Butt (gk), Hamit Altintop (67'), Holger Badstuber (70'), Toni Kroos (90'), Andreas Ottl, Anatoliy Tymoschuk, Miroslav Klose
Inter Julio Cesar (gk), Lucio, Maicon, Cristian Chivu (Nagatomo 86'), Andrea Ranocchia, Wesley Sneijder, Esteban Cambiasso, Dejan Stankovic (Coutinho 50'), Thiago Motta, Samuel Eto'o, Goran Pandev (Kharja 89')