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.
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But 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:
Awful howler in extra-time to give Atletico their first priceless away goal.
Exceptional in possession. A constant threat on the right-hand side.
Solid at the back as Atletico rarely threatened in normal time.
Led the back four superbly as ever.
A menace down the left. Went close to scoring in second-half when header crashed off the bar.
Busy in the middle of the park as Liverpool searched for goals.
The skipper marshalled the midfield well on his return to the side.
Took his first-half goal with aplomb to give Liverpool an all-important foothold in the tie.
Flitted in and out in attack but was always dangerous. Kept Lodi honest throughout. Wasted late chance in normal time.
A quieter night for the Brazilian before scoring second goal in extra-time.
A constant threat and looked likeliest to score for the hosts as ever.
An outstanding performance from first to last for the Slovenian as he almost single-handedly kept Liverpool at bay at times.
Struggled to get forward as Liverpool penned Atletico back.
Held his own well against Liverpool’s vaunted front three.
Headed everything as well as organising the back four impeccably.
Much like Trippier, struggled offensively but held his own against Salah on Liverpool’s right.
Typically busy and bought timely free-kicks time and again.
Another excellent midfield performance despite having less of the ball than normal. Went close from halfway in the second-half.
Energetic display in the middle of the park alongside Saul.
Did his defensive work diligently but failed to make huge impact when in possession.
A characteristically angry if not especially effective performance. Came in half-fit and looked like it.
Showed flashes of his quality on the rare occasions Atletico forayed into Liverpool’s final third.