Jurgen Klopp's side trailed 3-0 after the first leg at the Nou Camp but Divock Origi's seventh-minute opener gave Reds fans hope.
Georginio Wijnaldum came on as a half-time substitute and he repaid Klopp's faith with two goals in two minutes to put Liverpool 3-0 up and level on aggregate before Trent Alexander-Arnold's intuitive quick corner saw Origi net his second with 11 minutes remaining and complete a spectacular turnaround.
Here, Press Association Sport picks out some of the best images from a remarkable night at Anfield.
Roberto Firmino missed the match through injury (Peter Byrne/PA)
Mohamed Salah, who was also unavailable with concussion, arrived at Anfield wearing a t-shirt with the slogan 'Never Give Up' (Peter Byrne/PA)
Liverpool manager Jurgen Klopp, left, before kick-off (Peter Byrne/PA)
Lionel Messi, second left, clashed with Andrew Roberton, far right, during the early exchanges of the match (Peter Byrne/PA)
Divock Origi puts Liverpool ahead (Peter Byrne/PA)
Barcelona's former Liverpool striker Luis Suarez, left, reacts to a challenge from Fabinho (Peter Byrne/PA)
Liverpool captain Jordan Henderson picked up a knock in the first half but managed to play the full match (Peter Byrne/PA)
Robertson, right, was forced off at half-time with an injury (Peter Byrne/PA)
Barcelona manager Ernesto Valverde on the touchline during the first half (Peter Byrne/PA)
Wijnaldum scored Liverpool's second goal just nine minutes after coming on as a half-time substitute (Peter Byrne/PA)
Wijnaldum scored his second goal in two second-half minutes to level the tie (Peter Byrne/PA)
Alexander-Arnold's quick corner fell in the path of Origi to slot home Liverpool's fourth goal (Peter Byrne/PA)
Origi celebrates putting Liverpool 4-0 up (Peter Byrne/PA)
The scoreboard at Anfield (Peter Byrne/PA)
Messi speaks to referee Cuneyt Cakir after the defeat (Peter Byrne/PA)
Fabinho, left, and Virgil Van Dijk celebrate after the final whistle (Peter Byrne/PA)
Liverpool manager Jurgen Klopp celebrates after the match (Peter Byrne/PA)
Academy graduate Alexander-Arnold reacting after the stunning comeback (Peter Byrne/PA)
Salah, Klopp and Van Dijk celebrate in front of the Kop at Anfield (Peter Byrne/PA)
Liverpool celebrate their famous victory in front of the Kop (Peter Byrne/PA)
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