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|Bayern goalkeeper Manuel Neuer was partly at fault for Sadio Mane's opening goal. (AFP/Odd ANDERSEN)|
The Senegalese's stunning opener was quickly cancelled out by Joel Matip's own goal.
But Virgil van Dijk's towering header restored the visitors' lead 21 minutes from time and Mane added a third with a diving header of his own to which an ageing Bayern side had no response.
Here, AFP Sport looks at three things we learned from Liverpool's triumph at the Allianz Arena:
Mane steps out from Salah's shadow
As goals for Mohamed Salah have dried up of late, Mane has stood up when his side have most needed him.
An exquisite touch to control Van Dijk's raking pass, poise to round Manuel Neuer and calm to chip the ball into the empty net gave Liverpool control of the tie with an away goal.
A second for the Senegalese six minutes from time took his tally for the season to 19, 10 of which have come in his last 10 games.
Salah remains Liverpool's top scorer with 20, but only one of those has come in his past nine matches.
The Egyptian did at least provide the cross for Mane's second goal, but with Salah and Roberto Firmino again disappointing, Mane is currently the form man in Liverpool's famed front three.
England 3 Germany 0
Tottenham and Manchester City showed Liverpool the way by thrashing Borussia Dortmund and Schalke by a combined aggregate score of 14-2 to take their place in Friday's quarter-final draw.
The Reds had a far tougher task against a side that had reached the semi-finals for six of the past seven seasons and had not exited at the last 16 since 2011.
Bayern have roared back to form in the Bundesliga of late to usurp Dortmund at the top of the table, but this defeat had the air of the end of an era for much of the side that won the competition in 2012/13.
Neuer, Mats Hummels, Javi Martinez and Robert Lewandowski all into their thirties.
Arjen Robben has already announced he will be leaving the club in the summer and 35-year-old Franck Ribery is expected to follow.
None of that will matter to former Dortmund manager Jurgen Klopp who was able to enjoy a return to his homeland.
After a clean sweep of three Anglo-Bundesliga battles, all four Premier League sides have made the quarter-finals, with Manchester United also into the last eight, for the first time in a decade.
Van Dijk the difference maker
Liverpool feared the damage that Bayern could cause in the first leg without their suspended talismanic Dutch centre-back and the German champions lived to regret not cashing in with an away goal against a Van Dijk-less defence three weeks ago.
The world's most expensive defender has more than justified his £75 million transfer fee in 14 months at Anfield, but it was at the other end where Van Dijk decided the tie.
It was his pinpoint pass that picked out Mane for the opener and a towering header from James Milner's corner midway through the second half proved the knockout blow.