Liverpool went into the match trailing by a single goal from the first leg and, in a whit hot atmosphere, tried to press forward at every opportunity against a dogged Atltico defence, with the Spaniards appealing wildly every time a foul was committed. They came close to getting the goal they needed with Trent Alexander-Arnold whipped in a cross that just eluded Roberto Firmino, Jan Oblak making a fine reaction save. But he could do nothing to prevent Georginio Wijnaldums firm downward header from a cross by Alex Oxlade-Chamberlain two minutes before half-time which flew in to the net.
The second half was almost incessant pressure, with Oxlade-Chamberlain, Mo Salah and Sadio Man all going close, but the best chance fell to full-back Andy Robertson whose header hit the bar. Atltico offered little, but thought they had won the tie in injury time with a header from a free kick, but it was ruled out for offside.
With the match going into extra time, Liverpool extended their lead on the night when Wijnaldums cross was headed in by Roberto Firmino in a repeat of the first goal but then it all went wrong for the home side, with their goalkeeper Adrian at fault. He made a hash of a clearance, played it straight to Joao Felix and he picked out Marcos Llorente who shot past Adrian who compounded his error by slipping. And then Llorente tried his luck again from distance, although arguably Adrian could have done better again.
By this time Liverpool were completely deflated and, in injury time, Atltico broke clear through substitute Alvaro Morata who slipped the ball inside Adrians near post to complete a memorable night for the Spanish side.
Paris Saint-Germain beat Borussia Dortmund 2-0 in Paris to win their tie 3-2 on aggregate.
With the match played behind closed doors, and trailing 2-1 from the first leg in Germany, PSG levelled the overall tie thanks to their Brazilian forward Neymar, who headed in a cross from Angel Di Maria, with the Dortmund marking non-existent. And they extended their lead before half-time when Pablo Sarabias cross found full-back Juan Bernat who poked the ball into the net.
In the second half it was PSG who came closest to extending their lead, and the German side finished with only 10 men after Emre Can was shown a straight red card for violent conduct.