Liverpool have won 3-1 at the Allianz Arena to book their place in the Champions League quarter-finals.
Jurgen Klopp's men took the lead thanks to a brilliant goal from Sadio Mane, the man in form for the Reds.
During a cagey first-half, the Senegalese forward latched on to a ball from the Liverpool defence and completely deceived Manual Neuer as he sprinted out from goal.
With shades of Raheem Sterling against Manchester City in 2014, he delivered a fine left-footed chip into the open net.
However, the Bayern response came just minutes later, with Serge Gnabry causing damage on the right flank and firing across goal.
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Bayern Munich 1-3 Liverpool
Joel Matip was the unlucky party to make contact, prodding the ball past Alisson Becker and giving the Bavarians hope of turning things around.
Nevertheless, the away-goal rule ensured that Bayern needed to double their advantage and they put the visitors under immense pressure after the break.
Klopp was becoming increasingly frustrated with his midfield - to which Fabinho had been added early on - but the Reds' defence stood resolute.
Liverpool's goals in Germany
And it was Virgil van Dijk who eventually provided the breathing space that Liverpool needed, rising highest from a corner to head home.
It marked the 27-year-old's third goal of the season and none have been more important, necessitating than extra two goals from their German hosts.
Then Mane bagged a headed goal of his own to put the game to bed, his third in eight matches in Europe - prompting a mass exodus of Bayern fans.
Jurgen Klopp reacts
Speaking after the game, the Liverpool manager remarked: "I see it the same like all the boys in the dressing room, like how everybody sees it who is with us: it is a big night.
"We had a change early and we wanted to play more football than we did in the first half, so we changed that for the second half and it was much better.
"We scored an outstanding goal in the first half - an outstanding goal, wow. Conceded one as well, but I think after 45 minutes everybody knew it will not be easy for Munich; it’s possible, but will not be easy.
"The second half, I was really happy – not only because we scored two goals, but because we played football - how mature it was, how strong we looked, how good we defended.
"Bayern have so much quality, unbelievable – they are quick on the wings, strong everywhere, hard challenges and all that stuff, good in the last line, sensational goalkeeper – and we impressed them."
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