Arsenal scored two early goals in the first half to earn Mikel Arteta his first-ever win as a manager.
Manchester United came into the match with a spectacular display and taking possession but that was shortlived.
Nicolas Pepe broke the deadlock in the eighth minute when he thumped home a Sead Kolasinic’s cross.
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Pepe missed an opportunity to double the lead when his strike hit the woodwork shortly afterward.
Sokratis made it two before the half time break when he struck from cross range a Nicolas Pepe cross.
Goalkeeper Bernd Leno was rarely tested as the visitors were missing the services of Paul Pogba who is set to undergo surgery.
The win moved Mikel Arteta’s side to position ten with 27 points but they are facing the relegation side more than the top side.
Ole Gunner Solskjaer’s side hold the fifth position with 31 points, five points behind Chelsea who were held by Brighton earlier during the day.