All the pre-match hype had been over Danny Welbeck facing his former club, but the England forward had few opportunites to prove United boss Louis van Gaal wrong as United rode their luck before striking twice in the second half.
Antonio Valencia's shot was deflected in off Kieran Gibbs, whose collision with Wojciech Szczesny saw the Arsenal keeper substituted on 55 minutes before, as the Gunners pressed, Wayne Rooney clipped in a second on the break
Arsenal forward Olivier Giroud marked his return from three months out with a broken ankle by netting a well-struck consolation in stoppage-time.
It was a second-successive defeat for Arsenal, who had completely dominated the first half, but failed to beat David De Gea, who saved a one-on-one from Jack Wilshere - the latter later went off with an injured ankle.
While United will head back north with confidence renewed, Gunners boss Arsene Wenger was left facing the same questions about the direction of his side, now down in eighth place.
Things had looked like turning out so different following a blistering start by the hosts.
Alex Oxlade-Chamberlain was lively as he had been against Scotland on Tuesday night, holding off his England captain Rooney before darting to the right by-line and whipping a ball into the six-yard box, which Welbeck headed over.
The first key moment of the match came on 13 minutes when De Gea, who injured his hand while on international duty, made a hash of a clearance under pressure from Alexis Sanchez.
Aaron Ramsey collected the loose ball, which Welbeck laid off into the path of the onrushing Wilshere.
The England midfielder, though, ran it too close to De Gea, who blocked with his chest as unmarked Sanchez stood screaming for a square pass and a tap in.
United defender Luke Shaw had earlier injured his ankle, and eventually hobbled off to be replaced by Ashley Young on 16 minutes.
Referee Mike Dean had to give Wilshere and Marouane Fellaini a stern talking to after the pair needlessly squared up
The much shorter Arsenal man pushed his head into the United midfielder's chest - which on another day could well have been punished by a red card - and sparked a brief melee.
On 41 minutes, Di Maria scampered away down the right and fed Rooney, and it needed a timely sliding block from Chambers to prevent the England captain putting United ahead.
At the start of the second half, Welbeck was away again down the left, but after cutting into the penalty area, he could not beat De Gea at the near post.
Wilshere was left in a heap after a sliding challenge from McNair turned his ankle, and was eventually replaced by Santi Cazorla on 55 minutes.
United swept into the lead through some comedy defending from Arsenal, which would not have looked out of place on the set of 'Dumb and Dumber To', with American actors Jim Carrey and Jeff Daniels guests on the Emirates Stadium pitch before kick-off.
Goalkeeper Szczesny came out to palm away a deep cross from the left, but was clattered into by Gibbs.
The loose ball dropped to Valencia, who drilled his shot goalwards and which looked to be going wide but deflected off Gibbs, who was still on the ground, and into the net.
Szczesny had taken a heavy blow in the ribs, and was not able to continue, so Emiliano Martinez came on.
During the stoppage, there was an incident on the United bench, as substitute Darren Fletcher was involved in an angry exchange with Arsenal supporters in the rows immediately behind.
When play eventually restarted, Sanchez glanced a diving header straight at De Gea.
Arsenal, though, were made to pay for pressing such a high line as United added a second on the break.
Di Maria skipped away down the right, drawing Nacho Monreal out of position before squaring to Rooney, who ran into the area and clipped the ball over the goalkeeper.
Argentina forward Di Maria could have added a third early in the eight minutes of stoppage time after breaking clear from a corner, but floated the ball wide of the far post.
Giroud stunningly cracked the ball past the hand of De Gea into the top left corner from 20 yards, but a grandstand finale never came.
Source : PA
Source: PA