Manager Jurgen Klopp described the match as "unbelievable". Two-goal hero Georginio Wijnaldum said it "showed everything is possible in football".
Liverpool had just thumped mighty Barcelona 4-0 in yet another emotional European night at Anfield, overturning a 3-0 deficit from the first leg in Catalonia.
The semi-final tie had looked dead and buried, even with Liverpool's pedigree for coming back from the brink in European games.
Defeat in the first leg had been comprehensive. Two goals from Lionel Messi, including a stunning free kick that marked his 600th goal for Barcelona, and one from former Reds favourite Luiz Suarez at Camp Nou had left the Merseysiders facing a humbling exit.
A stunned Klopp admitted afterwards that Messi was "unstoppable" in that sort of form.
"I don't know if we can play much better," the German said. "I think it was the best away game in the Champions League – not only this year, last year included."
A week later, Messi and Co would head to England for the second leg in front of an Anfield crowd whose relentless backing would be the driving force behind an unforgettable evening.
Former England captain Alan Shearer told BBC Radio 5 Live: "I don't think I'll see or hear an atmosphere like this again. The atmosphere was just something that took my breath away."
Divock Origi started the wheels in motion with a crucial early goal, tapping home from close range after seven minutes.
But it was the quickfire double of substitute Wijnaldum just after half time that turned the match on its head.
First, the Dutchman met Trent Alexander-Arnold's low cross to smash home. Within 122 seconds, Liverpool were level on aggregate when Wijnaldum headed in a Xherdan Shaqiri cross to send Anfield wild.
Now the comeback was truly on, and Barca were buckling under the pressure. With 11 minutes left Alexander-Arnold again turned provider with a quick-thinking low corner into the box for Origi to fire home.
It was the first time since 1986 – when Barca knocked out Gothenburg – that a team had managed such a feat in the European Cup.
"If I have to describe this club then it's a big heart and tonight it was pounding like crazy," Klopp said after. "You could hear it all over the world.
"The whole game was too much," he added. "Winning is difficult but with a clean sheet, I don't know how they did it."
"It means so much to all of us ... creating this emotional atmosphere together is so special. It's all about the players.
"We know this club is the mix of atmosphere, emotion, desire and football quality. Cut off one and it doesn't work.
"I am really proud to be manager of this team. It's unbelievable what they did tonight. It's so special."
Wijnaldum admitted he was "really angry" to have been left on the bench by Klopp and was determined to make his mark after replacing the injured Andy Robertson at half time.
"People outside doubted us," the Dutch international said. "They thought we couldn't do it. But once again we showed everything is possible in football."
For Barcelona, it was a painful, if all-too familiar, story. The previous season, they had battered Roma 4-1 at Camp Nou in the quarter-final first leg, only to lose 3-0 in Italy to go out on away goals. They had last reached a Champions League final since 2015.
"We have to be ready for all the criticism that is going to rain down on us now," Suarez, who had been relentlessly jeered by Liverpool fans all night, said.
"We are very sad, we are in a lot of pain. For their fourth goal, we looked like schoolboys.
"We have to do a lot of self-criticism because this is the second time that the same thing has happened to us. We cannot commit the same mistake two years in a row."
Midfielder Sergio Busquets said: "I apologise to the fans because after the Rome thing, it happens again."
Manager Ernesto Valverde said: "I do not know how it's going to affect me. Here we are, the coach has to take responsibility.
"Things got on top of us after those two quick goals [from Wijnaldum]. We didn't manage to get on the scoresheet and they rolled us over really."
Just 24 hours later, Tottenham Hotspur produced their own semi-final comeback when Lucas Moura scored a dramatic 96th-minute winner to complete his hat-trick and earn Spurs an away-goals victory over Ajax.
Liverpool, who had lost the previous year's final to Real Madrid, were not to be denied this time round as goals from Mohamed Salah and Origi sealed their sixth European Cup. Fittingly, the final took place in Madrid.
But it was that deafening night at Anfield that will live long in the memory. "The whole game," an emotional Klopp said afterwards. "The whole performance was too much. It was overwhelming. I watched in my life so many football games but I can't remember many like this."
