Two goals from Sadio Mane helped Liverpool beat Bayern Munich at the Allianz Arena and reach the Champions League quarter-finals for the second successive season.
Neither side created many clear opportunities on a wet night in Munich and both sets of players were guilty of giving away possession too easily and too often.
However, the Reds carried more of a cutting edge and took the lead in the tie in the 26th minute when Mane displayed an exquisite touch to bring down Virgil van Dijk's raking pass before firing into an empty net after Manuel Neuer had rushed from his goal.
Bayern now needed at least two goals and pulled one back when Joel Matip turned into his own net from close range.
However, the expectant waves of attack from the German champions never materialised after the break, and Van Dijk all but ensured Liverpool's spot in the last eight when he powered home James Milner's corner.
Mane capped off an excellent display when he headed in his second six minutes from time. It was his 10th goal in the past 10 games.
The match ended on a slight sour note for Liverpool when full-back Andrew Robertson picked up a yellow card in stoppage time which means he will be suspended for the first leg of their quarter-final.
The Reds' win means there will be four representatives from the Premier League in the last eight for the first time since 2009.
Bayern's starting XI contained six players aged 30 and older and they lacked energy and ideas in attack. Liverpool, on the other hand, never needed to exert themselves too much bar a 15-minute period at the end of the first half.
The first quarter was cagey, mirroring the goalless first leg. The Reds adopted a hit-and-hope strategy to their front three which almost paid off when Roberto Firmino smacked a shot inches wide from Mohamed's Salah's hooked ball.
Two minutes later another hopeful ball resulted in the opener.
Van Dijk launched a long pass intended for Mane, whose instant control dumfounded both the tracking Rafinha and Neuer, who miscalculated his foray forward. Mane, with his back to the Germany keeper, turned and fired into the empty net.
It was a brilliant finish, but he benefited from Neuer's terrible judgement.
With the advantage of an away goal and Bayern lacking invention, the Reds should have seen out the rest of the half, but Niko Kovac's side hit back with their own hopeful ball forward from Niklas Sule.
The centre-back's pass found Serge Gnabry, whose low cross, intended for Robert Lewandowski, was unwittingly turned in by Matip.
Klopp's men must have expected a second-half onslaught but Bayern found it difficult to get behind Liverpool's backline.
Instead it was Liverpool who found the net again when Van Dijk leaped above Rafinha and Mats Hummels to nod home Milner's corner.
The shackles now off, the visitors scored a third when substitute Divock Origi found Salah on the right of the area. The Egypt forward lifted the ball to fellow forward Mane who headed home.
The Bundesliga leaders came into the match on the back of a 6-0 win over Wolfsburg, but against better opposition they struggled badly.
Aside from Matip's own goal, the five-time winners never once forced Alisson into making a good save. There were flashes of brilliance from former Arsenal winger Gnabry, but his more experienced team-mates Franck Ribery, James Rodriguez and Lewandowski failed to make an impact.
The closest Lewandowski came close to scoring was when he just failed to get a touch on Gnabry's low's delivery.