Dejan Lovren scored a heart-stopping stoppage-time header as Liverpool completed an astonishing comeback to beat Borussia Dortmund 4-3 and reach the Europa League semi-finals.
Held 1-1 in last week's first leg at the Westfalenstadion, Dortmund scored twice in nine minutes through Henrikh Mkhitaryan and Pierre-Emerick Aubameyang to take a firm grip on the tie.
After Divock Origi had given Liverpool a foothold, Marco Reus struck again for the visitors, but goals from Philippe Coutinho and Mamadou Sakho levelled the tie before Lovren headed home in the 91st minute to give former Dortmund coach Jurgen Klopp the biggest win of his Anfield tenure.
"It is difficult to explain. A wonderful, wonderful night at Anfield and to be honest the game was strange," Klopp told BT Sport.
"This is European football at its best. It's hard to believe. Congratulations to all of the lads.
"It is a game that all fans - even not of Liverpool or Dortmund - can say, 'OK, football is a nice game.'"
Liverpool's stirring rally, which unfurled amid an electrifying Anfield atmosphere, took them into a continental semi-final for the first time since 2010 and kept Klopp on course to end his first season at the club with a trophy.
His successor at Dortmund, Thomas Tuchel, could only look on in disbelief at the final whistle as the 5-4 aggregate scoreline condemned his side to defeat, four days on from a 2-2 draw with Schalke that left his men seven points adrift of leaders Bayern Munich in the Bundesliga.
Kick-off was preceded by a rousing communal rendition of 'You'll Never Walk Alone', the two clubs' anthem, and a solemnly observed minute's silence to mark the 27th anniversary of the Hillsborough disaster.
But any sense of sentimentality quickly vanished as Dortmund turned the tie on its head in the early stages.
An early Aubameyang effort that curled wide gave Klopp's side a warning and when the ball next found its way into the hosts' box, after a Liverpool attack broke down high on the left flank, there was no reprieve.
Gonzalo Castro's flighted cross picked out Aubameyang and although his close-range volley was alertly parried by Simon Mignolet, Mkhitaryan tucked in the rebound.
Sakho had played both Dortmund attackers onside and he was also at fault for the second goal as Aubameyang ran in behind him to collect Reus's delicately threaded pass and slam a shot into the top-right corner.