Jurgen Klopp’s men were on the end of a harsh 3-0 semi-final first leg defeat in Spain last week and faced a mountain to climb in order to ensure that they would be playing in the final in Madrid on June 1.
However, they took a big step towards hauling back the recently-crowned Spanish La Liga champions when Divock Origi scored an early goal to send the already noisy home supporters into raptures.
The atmosphere went up another notch when substitute Georginio Wijnaldum stunned Barca with two goals in as many minutes early in the second half to level the tie, before Origi scored his second 11 minutes from time to seal a sensational win.
It is only the third time in European Cup history a team has come back from a three-goal first leg deficit in the last-four and it sets them up for a second consecutive final appearance against either Tottenham or Ajax.
Liverpool boasted four changes from the 3-2 win at Newcastle on Saturday as Joel Matip, James Milner, Xherdan Shaqiri and Origi replaced Dejan Lovren, Wijnaldum, the injured Mohamed Salah and Daniel Sturridge.
Barca boss Ernesto Valverde named the same XI that won the first leg at the Camp Nou last Wednesday.
Lionel Messi tried to silence the Reds fans in the opening minutes when he went surging through towards goal only for Fabinho to deny him with a well-timed tackle.
However, it was the Reds who threw the tie back into the melting pot with the early goal they desired after just seven minutes.
Jordi Alba’s poor header gifted possession to Sadio Mane who flicked the ball on for Jordan Henderson and, while Marc-Andre ter Stegen did well to parry his strike, Origi was on hand to slot home the rebound for his first-ever Champions League goal.
Origi was almost gifted a quick second but he pulled out of a chase for the ball and allowed Ter Stegen to gather.
On nine minutes, Mane went down in the area under a challenge from Sergi Roberto, but the referee was quick to wave play on despite the appeals.
Barca recovered from their wobble and almost levelled on the night on 13 minutes when Messi got a shot away at goal only for Alisson to produce a fine save as he tipped the effort over the crossbar.
Alisson was on hand again five minutes later as he pushed away a Philippe Coutinho effort that was heading towards the bottom corner.
Andrew Robertson tested Ter Stegen with an effort from distance, before the Scotland international picked up a knock which ultimately forced him off at the break.
Wijnaldum replaced him during the break, but it didn’t have a negative impact on the Reds as they made a bright start to the second half as Ter Stegen did well to deny Virgil van Dijk from close range on 50 minutes.
It was game-on 54 minutes later when the Wijnaldum met a Trent Alexander-Arnold cross and hit a powerful low drive which flew under Ter Stegen’s body.
And, just two minutes later it was all-square at 3-3 on aggregate when Wijnaldum got up in the area to meet a Shaqiri cross and guided his header into the top corner past Ter Stegen to send Anfield absolutely crazy.
Liverpool gradually lost a little momentum from their two quick goals and Alisson was again called upon to make a good save to deny Messi who lashed a low strike across his goal on 69 minutes.
However, the hosts came back and unbelievably got the fourth goal to take the lead in the tie on 79 minutes when Alexander-Arnold was given time and space to pick out Origi on the edge of the six-yard box and he slammed in his second of the game into the far corner.
It was backs to the wall in the closing stages as Barca pressed for the away goal which would send them through, but the Reds held on to write another memorable page in the club's illustrious European history.