Liverpool completed a sensational comeback to dump Borussia Dortmund out of the Europa League, having been three goals down midway through the second half.
Although Jurgen Klopp's side came into the match with the advantage of having scored in Germany, Dortmund wiped it out almost instantaneously when Henrikh Mkhitaryan rifled home in the fifth minute, picking up the rebound from Pierre-Emerick Aubameyang's effort.
Aubameyang got in on the action less than five minutes later, conjuring a blistering finish after being released down the right flank by Marco Reus, and Liverpool were in shock.
The damage was contained there until half-time, however, and Divock Origi got the hosts back into it just after the break with a low shot underneath Roman Weidenfeller - but Dortmund restored their two-goal cushion when an incredible Mats Hummels pass found Reus to score.
Liverpool suddenly needed to find three more but, midway through the half, Philippe Coutinho completed a fine run by firing into the bottom corner from outside the box and Anfield erupted when Mamadou Sakho got the final touch on a corner with just over 10 minutes to go.
Just when it looked like that would not be enough, Dejan Lovren headed home in injury time to send the home fans - and Klopp - into raptures.
The tie had appeared dead and buried as Liverpool fell behind inside five minutes.
A quick break saw Shinji Kagawa – one of the visitors' two changes from the first leg – and Gonzalo Castro combine to set up Aubameyang, whose volley from six yards was pushed away by Simon Mignolet, allowing the onrushing Mkhitaryan to side-foot home the rebound.
It was quickly two for Dortmund after Reus impressively surged forward and found Aubameyang with a precise pass. The Gabon international did the rest, taking one touch prior to finding the top corner with a powerful finish.
Origi – selected ahead of Daniel Sturridge in attack as at Signal Iduna Park – had a shot deflected wide and Adam Lallana miskicked badly from a good opening as the hosts attempted to reply.
Origi flicked another effort wide and Roberto Firmino – Liverpool's only change from the tie in Germany - was off-target with a diving header.
At the other end, Aubameyang could not quite get enough on a sliding attempt and Simon Mignolet got down sharply to keep out Kagawa as Klopp's men, despite having made a spirited response, went into half-time with it all to do, having failed to test Dortmund keeper Weidenfeller.
Liverpool got back into the tie two minutes and 34 seconds after the restart when great midfield play from Emre Can resulted in Origi being sent through on goal and the Belgium international took one touch before slotting under Weidenfeller.
Hopes of a home comeback appeared to have been dashed by Reus in the 57th minute. Hummels brought the ball out from the back and slipped a great pass through to his Dortmund and Germany team-mate to convert with a confident first-time finish, prompting wild celebrations from Thomas Tuchel.
Klopp brought on Sturridge and Joe Allen just after the hour mark and Liverpool did strike with 24 minutes remaining. Coutinho played a neat one-two with James Milner and impressively found the bottom corner from the edge of the area.
Klopp was ecstatic on the touchline with 12 minutes remaining when an unmarked Sakho stooped low to head home a low Coutinho corner from inside the six-yard box, putting the Reds one goal away from the semi-finals.
And a famous comeback was complete when Sturridge found Milner, whose perfect cross to the back post was powered home by Lovren as Anfield erupted.