The Reds showed good ambition in the start of the game to take the match to United, going ahead through Daniel Agger's header, though thereafter they were a more defensive unit for the remainder of the first half.
Ji-Sung Park got the equalising goal for United after a mistake by Jose Enrique allowed Antonio Valencia room down the right, but Liverpool got their winner through Dirk Kuyt late on to reach the fifth round of the FA Cup.
Here are six things that the Anfield match taught us.
With just one goal from his 24 Liverpool appearances during the 2011-12 season so far, you could be forgiven for thinking Dirk Kuyt was a completely different player to the one who top-scored for the Reds last season.
But it was Kuyt who came up trumps for Liverpool in a big way against Manchester United, plundering his second of the season with a drilled first-time effort past David de Gea to secure a late victory for the Reds in the FA Cup.
He has been unlucky in some games, and woefully off-target in others—but all that was forgotten after 88 minutes at Anfield as the Dutch forward, who had come on just 25 minutes earlier, netted the decisive goal in the fourth round.
His first Premier League goal of the season against Wolves in midweek would be a nice way to follow it up.
Once upon a time, many fans could not comprehend how a Liverpool defence without Jamie Carragher in it would fare.
I'll be honest, the thought of Martin Skrtel playing regularly without the organiser Carragher beside him was not one of happiness—but Skrtel is in the form of his life right now, and his partnership with Daniel Agger has blossomed into arguably the finest in the Premier League.
In the absence of Carragher, Daniel Agger's natural leadership skills have become both more apparent and important—as have the organisational skills of Pepe Reina behind them—and the two centre-backs have been the rocks on which Kenny Dalglish's team is being built.
Both are strong, committed defenders and both are comfortable both on the deck and in the air—but they contrasting styles which complement each other extremely well, and the succession of matches alongside each other that they have managed to play over recent months has helped them gel and develop a good understanding of what the other will do.
Skrtel, right-footed, prefers to come out of the backline to nip in ahead of an attacker receiving the ball—not always wisely, it is true—while Agger, a leftie, covers the spaces behind.
The Dane will drive forward out of defence with the ball at his feet, while Skrtel generally keeps it short and quick with his passing—though, perhaps inspired by his team-mate, he has this season also launched raids forward the odd time.
Manchester City fans will point to Vincent Kompany and Joleon Lescott as rivals for the claim of the best defence in the league, but not while the latter is part of their first choice duo will they have a rightful claim to that crown.
Nemanja Vidic's absence rules any Manchester United pairing out of the running, while Spurs change their central defenders as often as Alex Ferguson changes his goalkeepers.
No, in Skrtel and Agger Liverpool have the best centre-back pairing as of right now—and long may that continue, in terms of form and fitness.
Alright, let's not go overboard.
But since the jibes about Luis Suarez continue—with regard to his hand-ball against Ghana in the World Cup, as well as other things—we might as well use his instinctive stop as a comparison to David de Gea's hesitant and nervous approach to goalkeeping.
Let's be clear; de Gea is a great shot-stopper, is pretty quick off his line and, when in form, has decent distribution.
But he has never been convincing at claiming high balls or dealing with the physical threat of attackers, and his errors this season have eroded away his confidence to such an extent that he is now calling for the referee's attention even before opponents arrive in his shadow, let alone before they start actually making contact.
de Gea was arguably at fault for both Liverpool goals in the FA Cup clash at Anfield; from Steven Gerrard's corner, he was so busy trying to push Andy Carroll out of the way that he ignored the actual ball coming towards him from Daniel Agger's head—the photo clearly shows the ball already past the Spanish goalkeeper before he is even reacting enough to raise his arms.
Rafael, positioned on the goal line, made a more convincing attempt to smother the effort on goal than de Gea did.
Later on he was beaten by a driven shot from Dirk Kuyt, which went well inside his near post and almost under his legs; the shot was fierce, yes, but almost straight at him, and his starting position was less than impressive, too.
It's a fair bet that Anders Lindegaard will be back in net for United's next Premier League encounter.
It wasn't as explosive a performance by the Liverpool striker as it was against the other half of Manchester in midweek, but Andy Carroll gave his best performance in some time for the Reds against Manchester United in the FA Cup.
He had almost nothing to work with in terms of service, balls played to feet and chances created for him to have a shooting opportunity, but Carroll worked hard for his team, laid off quick and simple passes to his teammates when he had the chance and caused several moments of near-embarrassment for Chris Smalling with some good control and strong hold-up play.
In addition, Carroll got the flick-on, which gave Dirk Kuyt the clear opportunity to win the game for Liverpool, which he took with aplomb.
One effort big Andy did get off in the game was with a late header from a narrow angle after a deep cross—but, not for the first time this season, he struck the woodwork instead.
If Carroll keeps the harder work-rate up and the improved touch going, the goals will come.
Much better. Not £35 million better, but certainly better.
After an up-and-down start to his Liverpool career, where he mixed his first Reds goal with some highly ineffectual displays, Jordan Henderson has been much-improved over the past couple of weeks with several accomplished performances in a more central role.
The former Sunderland man has not yet really dominated a game for Kenny Dalglish's side, but he is growing in stature and confidence and becoming an important link-man between midfield and attack with every passing game.
Against Manchester United he was seen popping up on both flanks as well as central, offering support to teammates wherever Liverpool happened to be attacking and doing plenty of good defensive work, too, tracking back and closing down the spaces in his own half.
It might be a slower upward trajectory than was hoped for with Henderson, but he is proving that he can fit into the Red shirt as time goes on, and further good performances will see him rewarded with regular starting spots in his preferred central midfield position.
Much, perhaps even far too much, of the pre-match build-up had centred around Patrice Evra and his return to Anfield.
Will he play? Should he play? Will he be targeted?
These and other such pointless questions were posed a thousand times over as the game drew closer, when in reality everybody knew that yes, he would play and yes, he would get stick from the Liverpool support.
That much was obvious.
And rightly so—Liverpool defend their own.
So the joy of the late, late winner for Liverpool against Manchester United, to knock their rivals out of the FA Cup, was enhanced perhaps just that small extra amount—because it was, of course, Patrice Evra who fell asleep at the vital moment.
Dirk Kuyt, on as a substitute, escaped the attentions of United captain Evra to sneak in on goal completely unmarked and blast home the winning goal with two minutes left on the clock.
Up in the crowd, Luis Suarez was wildly celebrating his team's winning goal and, presumably, looking forward to being able to take part in the FA Cup for the first time as the Reds progressed to the fifth round.
Maybe he'll write Evra a thank you note for helping him achieve that milestone.
For more reaction to the match, check out the Liverpool player ratings here.