The game scoreless from last month's first leg, Sadio Mane bagged a priceless away goal for the Reds - defeated in their last four away matches on the continent - which changed the complexion of the tie.
Bayern scored out of the blue when Joel Matip turned Serge Gnabry's cross into his own net, but Liverpool ensured that it was them, and not German champions Bayern, who would be in the hat for Friday's draw as Virgil van Dijk powered home a header and Mane added his second to make it a comfortable conclusion.
Here, Sports Mole rates the performances of Jurgen Klopp's side on a memorable night in Bavaria.
Alisson Becker: The most surprising thing about this standout last-16 tie was Bayern's lack of cutting edge across the 180 minutes. Alisson was beaten by Matip's own goal and had just a couple of saves to make, keeping out Lewandowski and Alaba from range. (7/10)
Trent Alexander-Arnold: Had a great tussle with experienced wideman Ribery down Liverpool's right. Was caught out a couple of times but ultimately kept both Ribery and substitute Coman away from goal. (7/10)
Joel Matip: A solid display on the whole and, while he did concede an own goal, it would have been a tap-in for Lewandowski if he had not attempted the interception. (7/10)
Virgil van Dijk: Yet another commanding performance from the Dutchman, who has suddenly added an attacking threat to his game. That is now three goals in his last four games for Liverpool in all competitions - more than he managed in his opening 55 appearances for the Reds (two) - and he also claimed an assist for Mane's opener. (9/10)
Andrew Robertson: Was arguably the player most at fault for Bayern's opener as Gnabry burst past him out wide and sent the ball into the middle for Matip to convert, but was also lively going forward and had a shot kept out at Neuer's front post. Biggest blemish of the night for Liverpool was the Scotsman's late caution, ruling him out of the quarter-final first leg. (7/10)
Georginio Wijnaldum: One of a number of players from both sides guilty of giving away the ball far too easily. Did not appear to do an awful lot, though a lot of his work goes under the radar, hence Klopp's decision to stick with him tonight. (6/10)
Jordan Henderson: The skipper's evening came to a premature end as he limped off 13 minutes into the match. His biggest involvement up to that point was a challenge with James, which led to his ankle injury. (5/10)
James Milner: Often described as 'Mr Reliable' by Liverpool supporters, though he has been far from his best in recent weeks. Improved as the match went on and sent in a delightful cross on the edge of the six-yard box for Van Dijk to power home. (7/10)
Mohamed Salah: In contrast to last season and the first two-thirds of this season, a lot of Salah's work is going unnoticed. Not on the scoresheet again today, but he helped out at times defensively and claimed an impressive assist for Mane's second. (8/10)
Roberto Firmino: Did well to help link up play in the final third, though he was guilty of dropping a little too deep at times. Was sloppy in possession when passing straight to Thiago early on but also had a couple of attempts of his own on a mixed night. (7/10)
Sadio Mane: Now Liverpool's all-time leading scorer in European Cup away games thanks to his brace in Bavaria. Took both goals very well, turning Neuer and clipping the ball into the far corner for the first and guiding a header away from the Bayern keeper for the late second. (9/10)
Fabinho: Many Liverpool fans wanted the Brazilian midfielder to start, and they pretty much got their wish as he came on early on for the injured Henderson. Performed well, though his biggest involvement in the match was a tackle on James to half the Colombian's run and earn himself a yellow card. (7/10)
Dick Origi: Was only on the pitch for 10 minutes but he played a big part in his side's final goal, spraying the ball to Salah who in turn picked out Mane. (7/10)
Adam Lallana: Produced his best display in a couple of years in the win over Burnley at the weekend but was given a late cameo role here with the victory already secured. (5/10)