Paris Saint-Germain produced a historic turnaround to progress to the Champions League quarter-finals at Liverpool's expense as they triumphed 4-1 on penalties after a 1-0 second leg win at Anfield.
Never in Liverpool's history had they lost a European tie after winning the first leg away from home but Ousmane Dembele's early strike brought the French champions level at 1-1 on aggregate.
PSG were then perfect with their four spot-kicks, while Gianluigi Donnarumma saved from Darwin Nunez and Curtis Jones.
Brilliant play by Alexis Mac Allister should have created the opener on four minutes when the Argentine's cross picked out Mohamed Salah, whose goalbound effort was deflected over by Nuno Mendes.
PSG took 10 minutes to ride out the storm from the home side before finding their feet.
The visitors took the lead on 12 minutes when Ibrahima Konate could only turn Bradley Barcola's cross beyond Alisson to leave Dembele with a simple finish.
The French international has now scored 23 goals in his last 17 games and could have had more before the end of the night.
PSG who had the better openings to extend their advantage before half-time.
Twice Alisson had to be at his sharpest to race off his line and save one-on-ones against Barcola and Dembele.
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PSG beat Liverpool to the signing of Khvicha Kvaratskhelia in January and the Georgian proved a constant menace to the Reds' defence.
Kvaratskhelia's shot from Dembele's cross was arrowing towards the top corner until a deflection from Ryan Gravenberch took it just over the crossbar.
Improved second-half performances have been a common theme of Slot's first season at Liverpool and the hosts came roaring out of the traps after the break.
Dominik Szoboszlai had a goal ruled out for offside against Luis Diaz earlier in the move.
Szoboszlai then had a goalbound effort blocked by Willian Pacho before Donnarumma made a vital stop from Diaz from the resulting corner.
Liverpool's momentum could have been halted by the loss of Trent Alexander-Arnold to a knee injury after the right-back landed awkwardly.
But his replacement, Jarell Quansah, was inches away from winning the tie when his header came back off the inside of the post.
PSG barely threatened during the second half of the 90 minutes but Liverpool were left hanging on for penalties in extra time.
Lucas Beraldo's header and Desire Doue's shot flew just wide before more Alisson heroics kept PSG at bay with a stunning stop to turn Dembele's curling effort round the post.
However, Alisson could not save them in the shootout as it was the other goalkeeper who was the hero.
Donnarumma produced great saves to deny Nunez and Jones, either side of four confident strikes from Vitinha, Goncalo Ramos, Dembele and Doue to send PSG into the last eight.
Harry Kane scored a goal and set up another as Bayern Munich won 2-0 at Bayer Leverkusen on Tuesday, going through to the Champions League quarter-finals 5-0 on aggregate.
Bayern were comfortable against last season's unbeaten German champions, having already done the damage with a dominant 3-0 win at home in the first leg.
With the match scoreless at half-time, Leverkusen rolled the dice in search of the goals they needed but it was Bayern who struck, with Kane waltzing through to tap in a Joshua Kimmich cross early in the second period.
With Leverkusen again pushing forward, the visitors added a second in the 71st minute, Alphonso Davies slamming a clever Kane chip low and hard to double Bayern's lead.
Kane, so often criticised for going missing in big games and scoring against the minnows, was again commanding, as he had been when scoring a brace in Munich.
The England captain showed finesse and physicality as he kept Bayern on track for a dream home final and a chance to exorcise the ghosts of their 2012 Champions League final loss to Chelsea.
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