It beat Barcelona 4-0 this morning, overturning a three-goal first-leg deficit and advancing to the final with a 4-3 aggregate victory.
Liverpool will play the winner of the other semifinal between Ajax Amsterdam and Tottenham Hotspur with the Dutch side leading 1-0 from the first-leg in London.
Liverpool, without injured strikers Mohamed Salah and Roberto Firmino, took a seventh-minute lead when a poor headed clearance from Jordi Alba fell at the feet of Jordan Henderson, who burst goalwards.
His low shot was parried out by Barca keeper Marc-Andre ter Stegen but straight to Divock Origi who slotted home.
The game took a remarkable turn following the introduction of Liverpool midfielder Georginio Wijnaldum at the break.
The Dutchman drove home a low cross from Trent Alexander-Arnold, which Barca keeper Ter Stegen should have saved, to make it 2-0.
Minutes later Wijnaldum rose to meet a Xherdan Shaqiri cross with a powerful header to make it 3-3 on aggregate.
Liverpool then grabbed an extraordinary fourth goal with a quickly-taken corner from Alexander-Arnold, catching the Barca defence asleep with a low ball that was turned in at the near post by Origi.
