Liverpool humiliated its fierce rival to pile more pressure on Red Devils boss Solskjaer, with Jurgen Klopp celebrating 200 wins as manager of the Merseyside club in dream fashion.
United was blown away as they went in at half-time four goals down for the first time in a Premier League game, making it all too easy for the Reds as Naby Keita and Diogo Jota were on target before Salah struck twice.
The magnificent Salah completed his hat-trick early in the second half, taking his goal tally for the season to 15, before substitute Pogba was dismissed for a poor challenge on Keita.
Salah has now scored in 10 consecutive games and Liverpool is unbeaten in 21 matches, while United is in disarray after the most chastening of defeats in its own backyard.
Keita silenced the United faithful when he capitalised on poor defending to slide beyond David de Gea with his right foot after being slipped in by Salah.
That strike in the fifth minute was the Reds' earliest at Old Trafford in the Premier League and they did not have long to wait for a second, Trent Alexander-Arnold's cross giving Jota a tap-in after a mix-up between Harry Maguire and Luke Shaw.
Liverpool, already without the injured Fabinho, lost James Milner midway through the first half but Salah put the Reds out of sight with a double before the break after Alisson had denied Mason Greenwood.
The abysmal Red Devils were all over the place and the ruthless Egypt forward made them pay, finishing with his right foot when he was picked out by Keita and tucking home with his left from close range just before a half-time whistle that was greeted with loud boos.
Salah completed his treble five minutes into the second half, racing onto Jordan Henderson's incisive pass before beating De Gea with a clinical left-foot finish after Cristiano Ronaldo had a goal ruled out for offside.
United's day took yet another turn for the worse when Pogba was dismissed for a reckless lunge on Keita following a VAR check, having initially been shown a yellow card on the hour mark.
Keita was unable to continue and the United players look like they would rather not, as only a brilliant save from De Gea prevented Alexander-Arnold adding a sixth.
Andrew Robertson's block sent the ball crashing against the crossbar late on to prevent Edinson Cavani from finding the back of the net and there were inevitably more boos at the final whistle to end a totally one-sided contest.