After a dominant opening period, the Red Devils took the lead just before the halftime whistle when Antonio Valencia nodded home a pinpoint cross from Ryan Giggs to give his side the lead.
However, the Gunners came out after the break looking a distinctively different team, and deservedly equalised in the 71st minute when Robin van Persie fired through Jonny Evans' legs and beyond Anders Lindegaard's despairing dive.
But with just nine minutes on the clock, Valencia made his way into the penalty area before sliding the ball back to Danny Welbeck, who smashed home the winner with aplomb.
Here, ESPNSTAR.com takes a look at the players that took the the Emirates on Sunday.
Wojciech Szczęsny - 7
An fairly error-prone performance from the Polish keeper, who at times hurled himself at the feet of the United strikers, showing disregard for his own safety.
Couldn't do much about United's two goals either.
Johan Djourou (off 46') - 3
This man has no sense of urgency whatsoever. No coincidence that the first goal was created from his side of the pitch as well, as he was exposed time and time again by the pace and trickery of Nani.
Laurent Koscielny - 7.5
Handled Welbeck well, not allowing him space and time on the ball. Ran his heart out in an attempt to get something from the game and was water tight at the back.
Per Mertesacker - 8
The Mertesacker Arsene Wenger signed must have been abducted by aliens, for the one that took to the field today won countless headers and showed superb positional sense. He even made a crucial goal line clearance from Welbeck's clever effort to keep the scores at 1-1.
Thomas Vermaelen - 6.5
At least there was some stability in the Arsenal back four with this man around, till that second goal when Valencia simply strolled into the penalty area to set up Welbeck. He switched off for a brief moment and Arsenal paid the price.
Tomas Rosicky - 6.5
Made a mockery of Arsenal's famous counter-attack in the first half, slowing down play as the Gunners looked to expose United on the break. There was a remarkable improvement in the second half though, when he created a brilliant opportunity for Van Persie to level the scores and even had a shot blocked off the line by Patrice Evra.
Alex Song - 7.5
Arsenal fans must be delighted Cameroon did not make the African Cup of Nations as he was the only player in midfield who was capable of breaking down United's play.
Alex Oxlade-Chamberlain (off 74') - 9
His first start for Arsenal in the Premier League was a really promising one. It was Chamberlain vs Manchester United for the entire first half, creating chances up front without shying away from his defensive duties. Great assist for Van Persie to level the scores.
Aaron Ramsey (off 84') - 5
Another woeful display from Ramsey who has plenty to learn from his fellow countryman. The Arsenal fans must be crying, wherefore art thou Jack Wilshere...
Theo Walcott - 5.5
Considering the legendary Thierry Henry is now back at the club, Walcott showed he doesn't deserve the number 14 jersey with performances like this week in week out. No more excuses for being young.
Robin Van Persie - 6.5
Barely had a touch of the ball in the first half, and when he had the goal at his mercy minutes after the restart, he fired it wide. Despite grabbing the equalizer, he didn't have a convincing game.
Nicholas Yennaris (on 46') - 6.5
A big game for the 18-year-old, who rose to the occasion and was way better at coping with Nani than Djourou.
Andrei Arshavin (on 74') - 5
The fans were not afraid to let their feelings be known when this change was made. Guess who allowed Valencia into the danger area so easily which led to United's second goal? Why fix that which is not broken Monsieur Wenger, considering Oxlade-Chamberlain had been stunning till then.
Park Chu-Young (on 84')
Once again, the Korea Republic captain was not given a decent opportunity to make an impact.
Anders Lindegaard - 6
Apart from the goal which no keeper would have saved, he was barely tested and looked fairly safe when coming out to claim high balls.
Jonny Evans - 7
Unfortunate to concede a goal between his legs but apart from that, Evans managed to put in a surprisingly error-free performance.
Chris Smalling - 8
A commanding figure in the air in the absence of Nemanja Vidic and Rio Ferdinand, winning almost all of the headers he went in to challenge.
Patrice Evra - 8.5
Excellent game from United's stand-in skipper, who defended reasonably well, but also charged forward and regularly kept the Gunners backline on their toes with his mazy dribbles.
Phil Jones (off 17') - 6
Another injury problem for Fergie to deal with after apparently twisting his ankle in the first 15 minutes of the match. Heartbreak for United fans.
Ryan Giggs - 6.5
Seemed to be of a different wavelength from his other team mates and was losing possession for United needlessly. He did however put in a quality ball into the danger area which resulted in his team's opener.
Michael Carrick - 7
Reasonable display from the England international, who retained possession well in the middle of the park.
Nani (74' off) - 7
Exposed Arsenal's weakest link in defence and made Djourou look like a kid. However, he did over-elaborate on numerous occasions when a simple first-time ball would have been the best option.
Antonio Valencia - 10
A great leap to beat Vermaelen in the air to hurt Arsenal just before the break. He singlehandedly won the game for United late on after his surging run into the danger area led to him setting up Welbeck for the winner.
Danny Welbeck - 8
Was a constant threat to the Arsenal defence, who - after having work so hard to get back into the game - left him with a clear shot on goal, and United's lead was restored.
Wayne Rooney - 7
Had an unproductive game in front of goal, but Rooney did well holding up play, especially in the latter parts of the game where his strength and control earned United a couple of freekicks, which helped ease the pressure.
Rafael (on 17', off 76') - 6.5
His battle of pace with Oxlade-Chamberlain provided an entertaining subplot to the game, although the Brazilian did have to tread carefully after picking up a first-half booking.
Paul Scholes (on 74') - 6
The returning legend didn't really make an impression after coming on, but with Henry missing, at least we got to witness one iconic figure take his place in this age-old rivalry.
Park Ji-Sung (on 76') - N/A
Brought on late in the game to add some energy and defensive awareness.