After Barcelona won the first leg 3-0 at the Nou Camp a week ago, few gave Liverpool a chance of scoring the goals they needed to progress, let alone preventing the La Liga champions from scoring themselves.
However, Divock Origi opened the floodgates in the first half and come second half, Georginio Wijnaldum scored two quick goals to level the match. three all in aggregate.
Origi completed a remarkable victory for Liverpool when he swept Trent Alexander-Arnold's low corner into the back of the net late on.
Meanwhile, Pep Guardiola, Jurgen Klopp, Mauricio Pochettino and Nuno Santo have been nominated for the Premier League’s manager of the season award.
Manchester City boss Guardiola could become only the third manager to retain the Premier League title after Sir Alex Ferguson and Jose Mourinho as his side bid to win an unprecedented domestic treble.
The Spaniard is being pushed hard for the title by Klopp with Liverpool already reaching the fourth-best points total of any team in a single PL season with one game to go.
Nuno has guided Wolves to a seventh-place finish and potential European qualification in their first season back in the Premier League.