Danny Welbeck netted the winner against his former side at the hour mark after Manchester United captain Wayne Rooney had cancelled out an early strike from Nacho Monreal.
While United boss Louis van Gaal made only one change from the Newcastle game as Luke Shaw came in for the suspended Jonny Evans, Arsenal made five alterations to their starting lineup, with Wojciech Szczesny , Nacho Monreal, Laurent Koscielny, Danny Welbeck and Alex Oxlade-Chamberlain coming in place of David Ospina, Kieran Gibbs, Gabriel Paulista, Olivier Giroud and Tomas Rosicky respectively.
The game started with Arsenal's Hector Bellerin going into the books in only the fourth minute after he brought down Ashley Young.
Young got an opportunity to put his side in front after he was teed up by Marouane Fellaini in the 20th minute, but the winger's effort sailed over the bar.
Moments later, some excellent work from Santi Cazorla allowed Welbeck to feed the ball towards Oxlade-Chamberlain on the right. The winger had a very good chance to pick out his teammates in the box, but his cross was poor and the opportunity was wasted.
However, the England winger made amends for his mistakes as he engineered the opening goal of the match in the 25th minute. Oxlade-Chamberlain, after avoiding a couple of tackles on the edge of the box, sent a good pass towards Monreal, who showed good composure as he slotted the ball past De Gea.
However, the Gunners joy was short-lived as United found the equaliser after only four minutes through Rooney. Angel Di Maria whipped an excellent cross into the box and the England striker made no mistakes as he headed the ball past Szczesny.
The Red Devils, who seemed boosted by the equaliser, threatened to take the lead in the closing stages of the first half as Szczesny was forced to make a good save to keep out an excellent effort from Di Maria.
Although, both sides struggled to create enough chances after the break, De Gea had to make an excellent keep out a deflected shot from Sanchez.
Di Maria got an excellent chance to put his side ahead after a goal kick from Szczesny was headed by Blind towards Fellaini. The Belgian picked out Di Maria with a chipped pass, but the Argentine was unable to hit the target.
The former Real Madrid man's miss proved very costly as Arsenal soon retook the lead through Welbeck in the 61st minute. A poor backpass from Valencia was intercepted by the England striker, who rounded up De Gea before tapping the ball into an empty net.
The Red Devils again nearly found the equaliser after only three minutes, but Chris Smalling was unable to keep his cool as he fired the ball over from close range.
De Gea then made an excellent save to deny Cazorla, but United's hopes of finding the equaliser evaporated after Di Maria was booked for diving and then shown a second yellow card for arguing and tugging the referee's shirt.