Louis van Gaal's side were deserved winners on the day, largely off the back of an excellent first half display, although the match as a contest was largely over shortly after the interval with the sending off of Steven Gerrard.
The Liverpool skipper had taken the captain's armband from Jordan Henderson just seconds before he was given his marching orders for a stamp on Ander Herrera, with a red card a just decision.
Emotion getting the better of Gerrard
Gerrard, coming on for Adam Lallana – who missed a glorious opportunity to level proceedings just before the break thanks to some great work from Henderson and Daniel Sturridge – was brought on to add some calm to Reds play following a frenetic first half, clearly let the emotion of the situation get to him.
Moments before, he went into a full-blooded challenge on Juan Mata and the temperature was raised inside Anfield, and while Herrera was booked for his involvement in the incident, a player of Gerrard's experience – any player in fact – can't expect to stay on the pitch after such an act.
That it happened in such a crucial game, against their biggest rivals both historically and currently for a Champions League spot, must be particularly galling for a Liverpool fan. A five-point gap is far from insurmountable at this stage of the season, but it makes Liverpool decided underdogs to qualify for the elite table of European competition again.
For United, it is simply a tremendous result, even though they failed to create much through their numerical advantage. Playing the whole of the second half against 10 men, the visitors were deserved victors thanks to their excellence in the first half, the opening half an hour in particular.
Liverpool nullified by visitors’ formation
Their formation nullified Liverpool throughout. On the flanks, the partnerships of Daley Blind and Ashley Young on the left and Antonio Valencia and Juan Mata on the right constantly created two-on-one situations against Raheem Sterling and Alberto Moreno.
Marouane Fellaini often drifted to the left to sometimes create a three-on-ones against Sterling, who didn’t have a great game at right wing-back and was a peripheral figure for the most part. The 20-year-old is a fantastically versatile figure but his defensive nous was tested throughout.
The opener came from one such an overload; United spread the play from one flank to the other and then back again, before Herrera eventually found Mata in a bit of space on the Liverpool right and the former Chelsea man broke the deadlock with an accurate finish Simon Mignolet could only get the faintest of touches to.
The Belgian was particularly difficult for Liverpool to deal with. He would win every header in an attacking position, allowing the on-rushing players to feed off the constant supply of knock-downs and second balls, which Liverpool were simply unable to deal with.
With Liverpool unable to get a foothold in the game, the Red Devils were well worth their lead.
This resulted in Lallana constantly having to drop deeper to receive the ball and as Liverpool were pressed, the pass-back to Mignolet was often the only outlet, which more often than not resulted in an erroneous goal kick and the loss of possession.
He might be something of an unsung hero in the Manchester United midfield but Michael Carrick is such an important player to the way they play. His metronomic passing keeps possession well and is a constant source of go-forward ball, but also anticipates danger well and helps out the defenders when and were needed.
Hosts respond well to going behind
To their credit, Brendan Rodgers side responded well to going behind and had their best spell of the game in the last 10 minutes of the first half, during which Lallana's chance was the most clear-cut.
That little spell, during which Liverpool got Sturridge and the Phillippe Coutinho more on the ball makes Gerrard's indiscretion after the break even more galling.
Mata's second was an even better finish than the first, and even though a spectacular bicycle kick was needed to bury the chance in Mignolet's net, it should be noted that the Spaniard again drifted in the little bit of space between Moreno and Mamadou Sakho, who, despite his crab-like nature, had another good game in a red shirt.
Sturridge gave Liverpool something to cheer about and a faint chance of rescuing something from the match with a sumptuous right-footed effort of his own, although David de Gea in the visiting goal should perhaps have done better at the near post.
By that time tactics had gone largely out the proverbial window and the rest of the match was marred by niggling fouls and off-the-ball incidents and both Mario Balotelli and Martin Skrtel were perhaps lucky not to be sent off as well.
As for the Phil Jones moment, a yellow card was probably deserved, although those sorts of challenges have been met with red cards before.
The hosts received a chance to make it 3-1 late on when Emre Can bundled over Blind and the referee had no hesitation to point to the spot. It was one of those which will always be a foul outside the box but doubt remains whether a goal-scoring opportunity was denied by the German's intervention.
Mata was denied the opportunity to score a historic hat-trick and it seemed almost fitting that Wayne Rooney, who had a shocking game in attack and in midfield, was unable to score his first Anfield goal in more than 12 hours.