Two goals each from stand-in forward Divock Origi and halftime substitute Georginio Wijnaldum left Lionel Messi and Barcelona utterly shell-shocked after a Liverpool performance full of passion, belief and determination.
Juergen Klopp’s side will play the winner of Wednesday’s other semi-final between Ajax Amsterdam and Tottenham Hotspur, with the Dutch side leading 1-0 from the first leg in London.
Liverpool became only the third team in the history of the European Cup or Champions League to come from three goals down after the first leg of a semi-final and progress after Panathinaikos in 1970-71 and Barcelona themselves in 1985-86.
It was a night that will be remembered by Liverpool fans alongside their fifth European Cup win in Istanbul in 2005, when they came back from 3-0 down at halftime to win on penalties.
For Barca, who went out on away goals to AS Roma in the quarter-finals last year, after winning the first-leg 4-1, it was a bitter occasion that will raise many questions for coach Ernesto Valverde.