Diego Forlan struck twice in two minutes as Liverpool succumbed to their first home defeat since before Christmas last year.
The Uruguayan's 65th-minute opener came after an abysmal mistake by Jerzy Dudek in the Liverpool goal.
And the United striker stretched the lead when he drove the ball past the Pole's inside post.
In a stunning climax to a typically tense encounter, Sami Hyypia cut the deficit to just one with eight minutes left.
Dietmar Hamann nearly levelled the scores with a 22-yard shot, which was acrobatically palmed on to the crossbar by Fabien Barthez.
But United held on for the win and cut the gap to league leaders Arsenal to six points.
After a fractious start to the contest, in which Ruud van Nistelrooy was booked for his challenge on Stephane Henchoz, United had the better of a scrappy opening half hour.
Despite a stunning Milan Baros half-volley in the second minute, which was well blocked by Barthez, the visitors looked far more willing to attack.
But none really created any danger, Ole Gunnar Solskjaer forcing the only real save from Dudek with his 30-yard rising strike.
The Norwegian international had earlier found the net, but he was marginally offside.
His second effort, in the 28th minute, finally triggered an initially static Liverpool, who had struggled with their passing and running off the ball, into life.
First Vladimir Smicer came close then Michael Owen looked to be through but a superbly-timed Gary Neville challenge forced the ball away.
After a dull start to the second half, van Nistelrooy created the first chance in the 63rd minute, but Jamie Carragher slid in to clear the danger.
The opening goal arrived two minutes later in the most atrocious circumstances.
Carragher headed the ball to Dudek, who let the ball slip under his legs, and Forlan pounced for a simple finish.
The Uruguayan striker passed the Polish keeper again two minutes later, this time into the right-hand corner after being put through by Ryan Giggs.
Liverpool unsuccesfully pushed forward in an attempt to cut the deficit for quarter of an hour before Hyypia drove the ball low past Barthez after a goal-mouth scramble.
The home side nearly equalised seconds later with Hamann's late attempt, but Barthez put in his match-winning save.
Liverpool: Dudek, Carragher, Henchoz, Hyypia,
Traore (Riise 78), Murphy, Gerrard, Hamann, Smicer (Diouf 70),
Baros (Heskey 59), Owen.
Subs Not Used: Diao, Kirkland.
Booked: Smicer.
Man Utd: Barthez, O'Shea, Brown, Gary Neville, Silvestre,
Solskjaer, Scholes, Fortune (Phil Neville 81), Giggs,
Forlan (Stewart 90), van Nistelrooy (May 90).
Subs Not Used: Chadwick, Ricardo.
Booked: Van Nistelrooy, Brown, Silvestre, Forlan.
Attendance: 44,250
Referee: A Wiley (Staffordshire).