Mohamed Salah became the first away player to score a hat-trick at Old Trafford for more than 18 years
On a day of acute embarrassment for United and Solskjaer, 10 years and one day since they lost 6-1 at home to Manchester City, Liverpool emphasised the vast gulf between the sides in brutal fashion.
Mohamed Salah was predictably their main tormentor as the Egypt forward claimed a hat-trick, the first of which meant he had scored for the 10th successive game.
Solskjaer cut a dejected figure as he and his players faced the full fury of their own fans, especially at half time, after an insipid and disorganised display.
The worrying signs were there for United after five minutes as Liverpool sliced them open when Salah set Naby Keita through to score at the Stretford End.
Diogo Jota then slid in at the back post unmarked to add a second from Trent Alexander-Arnold's delivery eight minutes later.
Liverpool were tearing United apart and the irresistible Salah got his first when he thumped the ball into the roof of the net from Keita's cross then beat David de Gea with a low effort to give Jurgen Klopp's side a four-goal half-time lead.
Many Manchester United fans left at the break and Solskjaer response was to send Paul Pogba on for Mason Greenwood, but on a day when nothing went right for United even that mainly cosmetic move backfired horribly.
Salah raced on to Jordan Henderson's superb pass to complete his treble five minutes after the break then Pogba was sent off for a reckless lunge at Keita that saw Liverpool's midfielder taken off on a stretcher.
The rest was a formality as Liverpool cruised to victory in front of thousands of empty red seats deserted by the home supporters.
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