The reigning champion Reds went ahead on aggregate when Georginio Wijnaldum headed home just before half-time.
Goalkeeper Jan Oblak repelled everything during waves of sustained pressure before Roberto Firmino looked to have scored the all-important winner in extra-time.
Yet, substitute Marcos Llorente first profited from an Adrian mistake to score the first away goal before stroking home a second.
Fellow sub Alvaro Morata wrapped things up with the last kick of the match to send Atletico through 4-2 on aggregate.
Here’s how every player rated:
Adrian – 4 out of 10
Awful howler in extra-time to give Atletico their first priceless away goal.
Trent Alexander-Arnold – 7
Exceptional in possession. A constant threat on the right-hand side.
Joe Gomez – 6
Solid at the back as Atletico rarely threatened in normal time.
Virgil van Dijk – 7
Led the back four superbly as ever.
Andrew Robertson – 7
A menace down the left. Went close to scoring in second-half when header crashed off the bar.
Alex Oxlade-Chamberlain – 6
Busy in the middle of the park as Liverpool searched for goals.
Jordan Henderson – 7
The skipper marshalled the midfield well on his return to the side.
Georginio Wijnaldum – 8
Took his first-half goal with aplomb to give Liverpool an all-important foothold in the tie.
Mohamed Salah – 6
Flitted in and out in attack but was always dangerous. Kept Lodi honest throughout. Wasted late chance in normal time.
Roberto Firmino – 7
A quieter night for the Brazilian before scoring second goal in extra-time.
Sadio Mane – 7
A constant threat and looked likeliest to score for the hosts as ever.
Jan Oblak – 9 Man of the Match
An outstanding performance from first to last for the Slovenian as he almost single-handedly kept Liverpool at bay at times.
Kieran Trippier – 6
Struggled to get forward as Liverpool penned Atletico back.
Stefan Savic – 7
Held his own well against Liverpool’s vaunted front three.
Felipe – 7
Headed everything as well as organising the back four impeccably.
Renan Lodi – 6
Much like Trippier, struggled offensively but held his own against Salah on Liverpool’s right.
Angel Correa – 7
Typically busy and bought timely free-kicks time and again.
Saul Niguez – 7
Another excellent midfield performance despite having less of the ball than normal. Went close from halfway in the second-half.
Thomas Partey – 6
Energetic display in the middle of the park alongside Saul.
Did his defensive work diligently but failed to make huge impact when in possession.
Diego Costa – 6
A characteristically angry if not especially effective performance. Came in half-fit and looked like it.
Joao Felix – 7
Showed flashes of his quality on the rare occasions Atletico forayed into Liverpool’s final third.