Fans and players were in tears as they dumped Lionel Messi and Barcelona out of the competition.
They will now face Tottenham or Ajax after doubles from Divock Origi and Georginio Wijnaldum.
Allez, Allez, Allez rang out as the emotional Liverpool supporters responded to what will go down as their greatest night at Anfield in recent years.
WHEN IS THE CHAMPIONS LEAGUE FINAL? DATE, VENUE ETC REVEALED
Liverpool faced an incredible task coming into the evening after losing 3-0 at the Nou Camp last week but turned the game on its head inside the opening seven minutes through Origi.
And then the second half exploded with half time substitute Wijnaldum scoring twice in 11 minutes to level the tie before Origi grabbed a stunning winner.
The crowd bellowed then famous song with Kenny Dalglish and co looking emotional in the stands.
Jurgen Klopp could hardly talk and his players were visibly moved by the reaction with James Milner crying on the pitch.
“The whole game was too much. It was overwhelming,” Klopp said. “We played against maybe the best team in world.
“Winning is difficult but winning with a clean sheet, I don’t know they did it. It’s unbelievable.
“I saw James Milner crying on the pitch after the game. It means so much to all of us.
“It’s the best phase of football. There are more important things in the world. But creating this emotional atmosphere together is so special. It’s all about the players.
“The mix of potential and unbelievable heart is just a mix I never saw before. You have to be confident in a game like this. Divock and [Xherdan] Shaqiri didn’t play a lot. Putting a performance in like that, it was so important. It shows what’s possible in football.”
He then dropped an F-bomb live on TV, when he said: “These boys are f***ing giants. Fine me for swearing if you want. These boys are GIANTS.”
Gary Lineker then refused to apologise for the bad language in the BT Sport studio.
“Well he’s certainly getting quite excited there,” Lineker said.
“I’ve been asked to apologise on behalf – I’m not going to. I think he’s perfectly entitled to after that.
“He can get away with it, it’s after 10 o’clock, after the watershed, well done Jurgen.”
Captain Jordan Henderson had gone down with an injury early and looked like he’d need to come off before battling on.
“Unbelievable,” Henderson said. “I don’t think many people gave us a chance. We knew it would be difficult but still possible.
“The belief we have in the changing room is amazing. We knew we could do something special at Anfield. Look at the fans and the lads – this is a special night. This is up there with the best.
“We wanted to start fast. We got an early goal which helped. It wasn’t just the goal, it was getting after them and putting them under pressure. We knew if we showed personality and heart then we’d have a chance.”
Andrew Robertson hit out at the Luis Suarez after he became pantomime villain at Anfield.
The Barcelona striker made the Liverpool fans furious with his antics in the first half after getting Fabinho booked and kicking Robertson and forcing him to go off injured.
“Who’s going to the final? We are,” Robertson said. “That’s all that matters. Gini went on [for me] and scored two. I don’t care right now.
“I’ve said so many times this season but what a team. We believe. People wrote us off. But we believed if we got off to a good start we could do it.
“Alisson has pulled off some unbelievable saves. Fingers crossed. We go to Sunday full of energy. It’s out of our hands but we’ve seen stranger things happen. Especially tonight.”