Harry Maguire's header in the 84th minute sealed one of United's most significant wins under coach Ruben Amorim and consigned Liverpool to a fourth straight defeat in all competitions.
The frustration of so many miserable experiences on Merseyside appeared to pour out of Maguire as the defender celebrated in front of United's travelling fans.
"It means everything. They've had the better of us over the last few years and we know that and it hasn't been good enough for our club," Maguire said.
"The old cliche is that it is only three points, but it definitely isn't. It means a lot more than that for the club, the boys and the fans."
Maguire's goal came late in another frenetic and thrilling match involving Liverpool in a season of dramatic finales for Arne Slot's team.
It is now three league games in a row in which Liverpool has been beaten by a goal scored in the last 10 minutes of regulation time or beyond. Before that, they had scraped to late wins of their own in six of the first seven games.
So while Maguire's headed goal maintained the losing trend, perhaps the biggest surprise was that there was not another twist in the tale.
There might have been when Cody Gakpo headed wide with an open goal to aim at and the fourth official indicated there would be eight minutes of added time.
The Dutch forward had already got Liverpool back on level terms in the 78th minute, poking in from close range after Bryan Mbeumo had fired United ahead inside two minutes.
Defeat leaves Liverpool fourth in the EPL standings, four points behind leaders Arsenal.
In the day's other Premier League match, Emi Buendia's curling shot sealed a 2-1 comeback win for Aston Villa at Tottenham.
The victory continued Villa's resurgence after a desperate start to the season and denied Spurs the chance to provisionally move up to second in the standings.
Buendia shimmied his way across the edge of the box in the 77th minute before sweeping a perfect shot low into the bottom corner.
It was Villa's fifth-straight win in all competitions after failing to pick up a victory in their first six games of the campaign.
It ended Spurs' seven-game unbeaten run that had looked set to continue when Rodrigo Bentancur fired hime after just five minutes.
Morgan Rogers leveled the game in the 37th minute before Villa went on to take all three points and consign Tottenham coach Thomas Frank to his second league loss since taking over from Aussie coach Ange Postecoglou in the summer.
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