Likewise, Brighton became the first visiting side since Arsenal in 2007 to score four times at Anfield, although the goals were not necessarily in the right net.
Kenny Dalglish had announced that this would be an audition for places in Sunday's Carling Cup final. In the theatre, the adage is that a great dress rehearsal means a calamitous first night. On this evidence, Cardiff City might fancy their chances at Wembley because, for all of Brighton's self-inflicted wounds, Liverpool were sometimes dazzling.
The Kop greeted the final whistle with a song about "putting the champagne on ice, we're going to Wembley twice". They had sung it in 2001, substituting Cardiff for Wembley and this season resembles that campaign conducted by Gérard Houllier. Liverpool may not be competing for championships but there are trophies on the horizon.
Steven Gerrard, a man who would instantly take silverware if asked to choose between trophies and the prize of Champions League qualification, produced a range of free-kicks, passes and crosses that spoke of a desperate hunger for success.
Morally, he deserved Liverpool's fourth but technically it was a second own goal by Liam Bridcutt, who tried to intercept Gerrard's shot from an acute angle but instead knocked it into his own net. Jamie Carragher, who once conceded two own goals against, of all teams Manchester United, would understand the midfielder's feelings.
It was not, however, the own goal most likely to be appearing on an end-of-season DVD. That fell to Lewis Dunk, who taking a cross from Luis Suarez on his thigh, played keepy-uppy with the ball until he had taken it over the line.
Frankly, neither he nor Brighton deserved to be humbled in this way, although they are not the first side to have put three balls into their own net in a single match. Sunderland have done it and so, too, have Portsmouth. It must be the sea air.
Liverpool thus reached the quarter-finals of a competition they have scarcely bothered with since Gerrard held the trophy aloft six years ago. The draw meant they would play all their games at home and that their opponents are Stoke City, who have not won a league fixture at Anfield since 1959, should simply fuel the optimism.
This might have been a tougher encounter than it proved. Brighton had earned their journey to Merseyside on the back of something that, with due deference to Paolo di Canio's tears of joy when Swindon overcame Wigan, has been unique in this season's competition. Brighton are the only club from the Football League to have knocked out a Premier League side that could realistically hope to win the FA Cup. Naturally, that side was Newcastle.
They had come this way before. In 1983, on their way to a final against Manchester United, Jimmy Melia's men had gone to Anfield and through a goal by Jimmy Case denied Bob Paisley his last chance of winning the FA Cup, the one trophy that was to always elude him as a manager. As the teams came out yesterday, a banner depicting Paisley confronted both teams. There was to be a revenge of sorts.
Brighton's opening moves were shot through with nerves. First Peter Brezovan, who was to enjoy a frantic evening in the visitors' goal, tipped over a shot from Stewart Downing. Those who jammed the Anfield Road End after the long journey from Sussex mocked Gerrard's delays in taking the corner but, when it arrived, Martin Skrtel, rushing in, met it with a flick of his shaved head at the near post and Dalglish greeted the goal in the same way he did when he scored them, with both arms aloft and a wide open grin.
The scoreline might not suggest it, but there were times when Brighton played and defended very well. Suarez, playing in front of the Brighton manager, Gus Poyet, whose impassioned defence of him in the Patrice Evra affair was far more convincing than anything Liverpool mounted, accelerated between two defenders and then unleashed a fierce shot that Inigo Calderon somehow cleared off the line.
Towards the end, when Liverpool were awarded a penalty for a foul on Dirk Kuyt, Dalglish indicated that Suarez should take it. As ever, the Liverpool manager probably wanted to make a point and support the Uruguayan at the same time.
His reward was a feeble spot kick that Brezovan had no difficulty saving, although Suarez did get his goal in the final moments, meeting a header from Andy Carroll from unmissable range. Carroll had scored his own, rather better, goal midway through the first half, meeting Downing's cross first time, a glimpse of the skill of which he is capable but rarely displays
Amid all the own goals, it was easy to forget that Brighton had equalised. The LuaLua brothers are one of the most positive things to have emerged from the inaptly named, Democratic Republic of Congo. On Saturday at Goodison Park, Blackpool's Lomana had seen Everton's Tim Howard turn a gorgeous drive on to the post. Here, his younger brother, Kazenga, sent a free-kick through the wall to beat Pepe Reina at his post for sheer pace.
Parity lasted until almost the interval as Suarez took Brezovan's punch away brilliantly under control, turned and shot. The keeper half-saved it again. Glen Johnson headed it goalwards and a combination of Sam Voakes and Bridcutt turned it home, although amid their embarrassment they were not to know there were to be two more in the wrong net.
Match facts
Liverpool: REINA 6/10; JOHNSON 7; CARRAGHER 6; SKRTEL 7; ENRIQUE 7; SUAREZ 7; GERRARD 8; HENDERSON 6; ADAM 7; DOWNING 7; CARROLL 7
Brighton: BREZOVAN 7; EL-ABD 5; DUNK 6; GREER 6; CALDERON 7; LUALUA 7; NAVARRO 5; BRIDCUTT 5; BUCKLEY 5; VOKES 6; BARNES 6
Substitutes: Liverpool Shelvey (Gerrard, 76), Kuyt (Henderson, 76), Rodriguez (Downing, 76). Brighton & Hove Albion Noone 5 (Buckley, h-t), Vicente 5 (El-Abd, 69), Mackail-Smith 5 (Vokes, 69)..
Booked: Brighton Navarro.
Man of the match Gerrard.
Match rating 7/10.
Possession: Liverpool 55% Brighton 45%.
Attempts on target: Liverpool 15 Brighton 4.
Referee A Marriner (West Midlands). Attendance 43,940.
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