Dejan Lovren scored a heart-stopping stoppage-time header as Liverpool completed an astonishing comeback to beat Borussia Dortmund 4-3 on Thursday 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 leveled 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.
"I can't explain," said Tuchel. "I could explain something logical. That wasn't logical.
"With the equalizer, it was an atmosphere where everybody, except our supporters, believed it was meant to be."
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.
Klopp had been bold in his team selection, bringing in Roberto Firmino for the injured Jordan Henderson, and while it left Liverpool light in central midfield, after the early shock had subsided they began to make chances.
Origi, preferred up front to Daniel Sturridge, had a shot blocked and flicked a half-volley wide, Alberto Moreno miscued a volley, Adam Lallana produced an embarrassing air-kick and Firmino steered a header wide, while Coutinho saw a drilled effort deflect behind.
Liverpool needed an early goal in the second half and they got it in the 48th minute, Emre Can exchanging passes with first James Milner and then Firmino before releasing Origi to prod his fourth goal in three games past Roman Weidenfeller.
No sooner had the hosts closed in than Dortmund accelerated again, Mats Hummels taking Liverpool right-back Nathaniel Clyne out of the game with an exquisite pass and Reus nervelessly beating Mignolet.
Coutinho reduced the arrears again with a low strike into the bottom-right corner before Sakho atoned for his earlier misdemeanors by bludgeoning a header into the net from Coutinho's corner.
It set up a breathless climax that culminated in Croatian centre-back Lovren climbing at the back post to nod in Milner's cross from the right and set the seal on an unforgettable Anfield night.