Liverpool took the early lead against the run of play after Daniel Agger found David de Gea's goalkeeping skills wanting. United equalised through an excellent goal by Park Ji-sung, who took a first-time shot after being set up by Rafael's cross from the right.
The home side upped the pressure in the second half and it paid off after Patrice Evra had a lapse of concentration that allowed Andy Carroll's flick-on to find an unmarked Drik Kuyt to finish two minutes from time.
Pepe Reina - 7.5
Solid and strong in a way fellow Spaniard and opposite number David De Gea so obviously wasn't.
Jose Enrique - 6.5
Shrugged aside too easily by Rafael in build-up to United's goal but had a decent game otherwise.
Daniel Agger - 8
Exploited poor defending at a corner and rose well to head the opener. Steady in defence as well.
Maxi Rodriguez (off 62) - 6
A rather impotent display from him today, lots of running and covering but nothing fruitful in the attack.
Jamie Carragher (off 62) - 7
Played an important role for Liverpool sitting in front of the defence and crowding the midfield out. Welbeck hardly got a sniff of the ball in the first half due to his efforts.
Martin Kelly - 7.5
Who needs Johnson when you have Kelly? The youngster proved himself every bit as good as, or better than Liverpool's regular right back in both defence and attack. Managed to handle Giggs well and contributed to the attack regularly as well.
Martin Skrtel - 7
A steady performance for the center back and was unlucky to have been breached by an excellent Park goal. He was also in right place to nick the ball away from Welbeck when he was about to tap into an empty net.
Jordan Henderson - 6
Should have done more given that he was deployed in a central position he is more familiar with. Some decent attack but Henderson hasn't shown why he was so highly rated in the first place.
Steven Gerrard (off 72) - 6
A strangely quiet performance from Gerrard after being crowded out in midfield by Scholes, Carrick and Giggs. Not his fault though, as he was instructed to hang back in the first half.
Stewart Downing - 6
Did well to get into dangerous positions to place the ball in the box but his delivery still isn't quite the finished product as shown in a particular youtube video.
Andy Carroll - 7.5
He finally showed Liverpool fans what he should be doing. An excellent match by his recent standards, striking the terror of physical English football into De Gea early in the game and testing the keeper's confidence all the time. Flicked on the ball for Liverpool's final goal.
Dirk Kuyt (on 62) - 7.5
Hat-trick hero last season and produced the decisive strike this time around.
Charlie Adam (on 62) - 6.5
Came on and helped Liverpool take control of the midfield.
Craig Bellamy (on 72) - 7.5
Provided the spark for Liverpool as they sparked to life after he came on.
David De Gea - 4
Proved that he isn't quite Premier League material with a below-par performance. He seemed rattle right from the first corner when Carroll was barging into him and was nervy after that. Allowd the first goal too easily when the ball literally went through his hair on the way in.
Patrice Evra - 5
Had a half-decent game otherwise considering the pressure he was under but he just had to be the one to slip up at the end. That shouldn't be happening, especially when he's a veteran in the team.
Jonny Evans - 6.5
Should have done better challenging for the ball in the first goal but Evans was very cool under pressure from Carroll otherwise. If the bumbling Evans turned up, he would have given a goal or two away already.
Chris Smalling - 7
A steady performance by Smalling which could see him nail a spot in the starting XI until the return of Nemanja Vidic. Not bothered by Carroll's presence and was tidy throughout.
Park Ji-sung - 7.5
An well-taken goal to reward the hardworking Korean to score United's first goal. Kept running trying to link up the midfield to attack but was easily nullified after being crowded out.
Michael Carrick - 5.5
Calm performance from Carrick in the first half but crumbled after Scholes went off. He was virtually anonymous in the seconf half except when he played a bad pass that cost Rafael a booking.
Rafael da Silva - 8
One of his best outings in a United jersey after this performance, chasing down Enrique to create the first goal while doing his defensive dutied well. Combined well with Valencia down the right wing to balance between defence and attack.
Paul Scholes (off 75) - 8
Gave another lesson on how to keep the ball in midfield. In the first half, Paul Scholes made 75 passes and completed 73 of them (97%). He was such a thorn in Liverpool's side that Carroll was ordered to stick close to him in the second half to prevent his passing game.
Ryan Giggs (off 89) - 6.5
The veteran Welshman was average but not for the want of trying. He tried to penetrate down the left wing but was stopped by an excellent Kelly instead.
Antonio Valencia - 8
Valencia is enjoying a return to the form that saw him become a crucial part of United's title push last season. He was their main avenue of attack and struck the post with a powerful shot in the first half.
Danny Welbeck - 5
He was severely cut off from the rest of his teammates due to Liverpool's excellent defenders and hardly had a sniff on goal.
Javier Hernandez (on 75) - N/A
Dimitar Berbatov (on 89) - N/A