The result took United two points clear of Arsenal again, with both teams left with seven games this season.
Park Ji-Sung headed home the winner after an hour, securing the spoils after Wayne Rooney's 33rd goal of the season had controversially levelled Fernando Torres' fifth-minute opener at Old Trafford.
Although victory was not achieved without a nervy ending, during which Torres spurned a glorious chance to equalise, the result kept United's noses in front of their title rivals.
For Liverpool though, fight was not enough.
When they scored four times in the corresponding fixture last season, it appeared to open the door to that championship Holy Grail.
Not only has that been proved fool's gold, a 10th defeat of the season leaves them requiring slip-ups from Tottenham and others just to finish in a Champions League spot. What Rafael Benitez claimed before Christmas was a guaranteed fourth-place finish could hardly be further away.
Sir Alex Ferguson once claimed that a game of tiddlywinks between what the majority still believe to be England's biggest clubs could trigger the deepest of passions.
Certainly there was no sense of inferiority from the visitors despite their present status, and with good reason.
It was the Merseysiders who had won the last three meetings - each of which featured the dismissal of Nemanja Vidic, who it seems in Torres has found someone he simply cannot handle.
Such is the mystique surrounding that duel there was an audible gasp the first time Torres ran at the Serbian. Like so much of the opening period's final half-hour, it petered out disappointingly. The spark had been ignited long before that, although Torres was the one who flicked the switch.
By his very demeanour, Torres gave the impression of being a man on a mission.
Five minutes into the contest, he seized on the loose ball after Michael Carrick had lost possession, sending Steven Gerrard away at top speed with an inspired backheel.
As Gerrard found Dirk Kuyt to his right, Torres continued his own run, United's defence never set properly to ensure the Spaniard remained under their control.
By the time Kuyt dug out his cross, Torres was on his own.
Park's wayward effort from a similar position later on proved the goal was anything but the routine effort it looked to be as the Spanish star guided the ball out of Edwin van der Sar's reach.
Quite apart from falling behind against such fierce rivals, an increasingly enthralling title race demanded a United comeback.
For Liverpool, the equaliser came far too quickly. The controversy was immediate too.
Benitez argued Javier Mascherano's attempt to haul back Antonio Valencia was outside the box, which, indeed, was where the infringement began. Ferguson countered the combative midfielder had prevented a clear goalscoring opportunity.
The managers - no friends these two - continued their finger-jabbing row long after Wayne Rooney had tucked home the rebound from a spot-kick awarded by Howard Webb and saved by Pepe Reina.
That was it for the goal threat until the hour mark arrived.
During his long career, Gary Neville has gone on plenty of unselfish runs down the right wing, knowing David Beckham or, more latterly, Cristiano Ronaldo were never going to give him the ball.
Darren Fletcher is not quite of that attacking calibre but Neville must have sensed his run was purely to provide space for the Scot.
So it proved. As Neville flew past on the overlap, Emiliano Insua edged to his right. In an instant, Fletcher had exploited the gap and curled over a cross.
As Rooney and Jamie Carragher tussled and tugged, Park arrived behind them, launching himself at the ball like a guided missile and powering the diving header into the corner of Reina's goal.
Rooney had one more chance before the end, which he fired wide.
Torres was on the end of a far better one when Steven Gerrard drilled over a low cross near the end.
For once against United, the Spaniard miscued and Yossi Benayoun headed the loose ball straight at Edwin van der Sar.
United could celebrate, Neville and Ferguson doing the cheerleading.
Liverpool's money men are staring at a big black hole marked Champions League, Benitez is failing on his guarantees.