Off-field matters had dominated pre-match proceedings as both sides tried to ease tensions ahead of the first meeting of the two sides since Luis Suarez's eight-match ban for racially abusing Patrice Evra.
But while there was plenty of animosity in the ground between rival fans, the match itself, somewhat unusually, contained very few flashpoints.
With Suarez still banned, Evra became the focal point, and it was his failure to get to Andy Carroll's flick-on first that put Kuyt through to fire the clincher in the 88th minute.
Prior to that it appeared the tie was heading towards a replay neither manager really wanted, after Park Ji-Sung had cancelled out Daniel Agger's header in the first half.
Evra's every touch was roundly booed, with the left-back also subjected to chants claiming his evidence to the Football Association's disciplinary commission had not been entirely reliable.
The United captain took it all in his stride, particularly in a strong challenge from Stewart Downing, but the temperament of goalkeeper David de Gea was more open to question.
On his last visit to Anfield the Spaniard had produced an impressive display to earn United a 1-1 draw, but after one early save from Maxi Rodriguez he began to look slightly more shaky on his first appearance in 2012.
De Gea would have been relieved to see Jose Enrique's long-range strike deflect behind off Chris Smalling.
But he exposed himself to criticism at the resulting corner as his preoccupation with trying to push Carroll out of his way allowed Agger to rise highest to head home Gerrard's cross.
Just moments earlier United had almost taken the lead when Antonio Valencia cut in from the right to fire a shot past Reina which rebounded back off his right-hand post.
Jamie Carragher, on his 34th birthday, was brought into the starting line-up, but an unfamiliar holding role in front of the back four for the Anfield veteran handed the midfield initiative to the visitors.
Following the opening goal United enjoyed a long spell of possession, knocking the ball around in midfield without any end product.
But just when they looked like squandering their dominance they equalised as Rafael da Silva shrugged off Enrique far too easily to get to the byline and drill over a low cross from the right which Park smashed first time past Reina, into the bottom right corner.
Early in the second half Ryan Giggs' cross from the left to the far post resulted in a moment of panic for Agger, but the Denmark international cleared with his knee under pressure from Valencia.
Chris Smalling had a similar episode of concern as he slipped when dealing with Enrique's pass into the penalty area, with Carroll's appeal for hands after he smashed the ball at the centre-back falling on deaf ears.
As the game started to open up Michael Carrick's defence-splitting pass saw Danny Welbeck knock the ball past Reina but Martin Skrtel got back to clear as the shot trickled goalwards.
The Carragher experiment was brought to an end in the 63rd minute when he was replaced by Kuyt, while Charlie Adam came on for Rodriguez.
De Gea's difficult afternoon continued as he allowed a Downing cross to slip through his fingers for a corner, although he managed to hold on from a Gerrard free-kick.
With 18 minutes remaining Craig Bellamy, the midweek hero against Manchester City in the Carling Cup, surprisingly replaced Gerrard, before Adam sent a long-range strike wide and Kuyt put a weak header from Downing's cross off target.
The Holland international made up for his miss two minutes from time when he popped up with the winner.
Reina's punt downfield was flicked on by Carroll and Kuyt got ahead of Evra to fire past De Gea.
It was only his second goal of the season, his other coming in the Carling Cup, but was as vital as the hat-trick he scored on this ground in the victory over against United last season.
Kuyt could have put the result beyond doubt moments later when Carroll crashed a header against the angle of post and crossbar but the striker stabbed the rebound wide.
The visitors looked for a way back in the closing stages but there was not enough time to respond.
Liverpool duly extended their unbeaten run at home to United to five matches, making up for some of the hurt felt after their third-round exit at Old Trafford a year ago in what was manager Kenny Dalglish's first match back in his second spell in charge.
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