Liverpool's hold on the Champions League was wrestled from their grasp after a dramatic last-16 second leg went into extra time at Anfield - and a finely balanced game turned on catastrophic blunder by goalkeeper Adrian.
Jurgen Klopp's side - seeking to win the trophy for a seventh time - thought they had overturned Atletico's 1-0 advantage from the first leg when Roberto Firmino's first goal at Anfield this season at the start of the added 30 minutes gave them the lead in the tie.
Georginio Wijnaldum's first-half header was full reward for Liverpool laying siege to the Atletico goal for much of the first 90 minutes.
And yet, as the Kop sensed another memorable Champions League victory, Adrian - deputising for the injured Alisson - paid the price for a dreadful clearance as substitute Marco Llorente pounced with a low finish to secure Atletico's crucial away goal.
Llorente struck again with another composed finish in the 105th minute and with the spirit draining out of Liverpool and their supporters, former Chelsea striker Alvaro Morata adding insult to injury with a third in the dying seconds to send Atletico through to the last eight.
Elsewhere, Paris St-Germain rid themselves of their Champions League curse as they overturned a 2-1 deficit against Borussia Dortmund inside an empty Parc des Princes to reach the last eight.
Concerns over the coronavirus meant fans were barred, but many gathered outside the stadium and celebrated when Neymar headed PSG into the lead.
Juan Bernat made it 3-2 on aggregate when he turned in Pablo Sarabia's ball.
Dortmund's Emre Can saw red late on after two bookings in quick succession.
PSG's players celebrated wildly at full-time before greeting the hundreds of supporters who remained outside the Parc des Princes.