Kuyt opened the scoring in the heavyweight Premier League clash on 34 minutes, firing home from a yard out after great work from Luis Suarez.
His second arrived just five minutes later when the Dutchman capitalised on a poor defensive header from Nani.
And he completed his treble in the 65th minute – blasting gleefully into the net in front of the Kop from no more than two yards after Edwin van der Sar had failed to hold onto the impressive Suarez’s free-kick.
The Reds also handed record £35million signing Andy Carroll a 74th-minute debut off the bench and he showed some useful touches on a dream afternoon for the Merseysiders.
Javier Hernandez had the final say when he headed in Ryan Giggs’ cross from 10 yards.
United remain top of the table by three points from Arsenal, who have a game in hand on Sir Alex Ferguson’s side. The win, meanwhile, lifts Liverpool up to sixth.
Liverpool’s fully deserved victory over United may not ultimately prevent their arch-rivals surpassing the Reds’ 18 league titles at the end of the season.
It has, however, dented Sir Alex Ferguson’s side’s hopes of a straightforward run-in and at the same time restored some pride for the Reds after two defeats at Old Trafford already this campaign.
Kuyt grabbed the headlines with a first Liverpool hat-trick against United since Peter Beardsley’s in September 1990, before Hernandez headed an injury-time consolation – but there were many more who deserved the plaudits.
Tireless livewire Suarez had a hand in all three goals while Lucas and Raul Meireles produced impressive midfield performances.
The afternoon was capped off with a long-awaited debut for Carroll after more than two months on the sidelines with a thigh injury.
For United their second-choice central defensive partnership of Wes Brown and Chris Smalling, deputising for the suspended Nemanja Vidic and injured Rio Ferdinand, never looked comfortable on an afternoon when very few of visiting team reached anywhere near the exacting standards Ferguson demands.
They still remain top of the table, and it is difficult to bet against them being in that position come May, but two defeats in five days – having lost at Chelsea in midweek – leave plenty of questions to be answered.
While Carroll had claimed all the adulation prior to kick-off, when the action got going it was his fellow January arrival Suarez who had an effect where it mattered most.
The Uruguay international, a £22.7million transfer from Ajax, had one early effort prodded at van der Sar but that was merely a precursor to a piece of brilliance to set up the opener.
When he collected the ball on the left of the penalty area his route to goal was blocked by a number of opponents but his quick feet saw him weave past Rafael, Michael Carrick and Wes Brown on his way to the byline.
From there he squared the ball through Van der Sar’s legs to present Kuyt with a tap-in from just inches.
Suarez could claim to have had a hand in the next one too – but the main credit had to go to Nani, who had a defensive aberration.
The Portugal international inexplicably headed the Uruguayan’s cross back into his own six-yard area where Kuyt gleefully nodded in.
Liverpool’s lead was fully deserved but it had been United who had come closest to scoring prior to Kuyt’s 34th-minute strike.
Dimitar Berbatov, scorer of a match-winning hat-trick in their Old Trafford league encounter, volleyed Wayne Rooney’s knockdown against the outside of Jose Reina’s right-hand post.
The rivalry between the teams, England’s dominant pairing over the last four decades, was evident in the closing stages of the first half.
Jamie Carragher, switched to right-back after Fabio Aurelio went off injured, was lucky to escape with just a booking after a reckless shin-high tackle on Nani.
After the ensuing melee, Nani departed on a stretcher, replaced by Javier Hernandez, and Van der Sar was cautioned.
Rafael also benefited from referee Phil Dowd’s leniency after a high challenge on Lucas Leiva earned him, and Martin Skrtel for his retaliation, a booking.
The second half began with United, not unexpectedly, having their best spell and for 20 minutes it appeared a goal was imminent.
Giggs, breaking Sir Bobby Charlton’s record of 606 league appearances, met Rooney’s cross with a first-time shot which whistled just over the crossbar to serve as a warning that the game was far from finished.
Meireles had to clear off the line for the second time in the match to prevent Berbatov’s close-range header going in while Giggs curled an 18-yard free-kick over.
More gaps were appearing in the visitors’ defence, though, and when Kuyt put Meireles clean through Van der Sar came to the rescue by palming his angled shot away.
The Dutchman was at fault in the 65th minute, however, when he spilled Suarez’s free-kick and his compatriot knocked in the rebound.
Carroll’s long-awaited debut arrived in the 74th minute when he replaced Meireles to a rapturous reception and his first touch was a goalbound header.
Kuyt’s supreme confidence saw him attempt a 25-yard volley which screamed wide while Gerrard twice hit low shots either side of each post.
Hernandez scored a late headed consolation from Giggs’ cross in added time but it hardly raised a cheer among the visiting fans.