Goals from Antonio Valencia (4') and Jesse Lingard (11', 63') are enough to see Jose Mourinho's side come away from the Emirates with all three points. Alexandre Lacazette (49') scored a consolation goal for the Gunners.
But that win has come at a cost after Paul Pogba was sent off for a straight red card in the 74th minute. That will see the French midfielder suspended for the Manchester Derby.
The result sees Arsenal drop to 5th while United close the gap on City to 5 points although Pep Guardiola's side has a game in hand.
Man of the Match? Certainly David De Gea with 14 saves - the most by a goalkeeper in the Premier League this season.David De Gea made 14 saves!
90+5' There's just no way through for Arsenal at the moment with 8 United players in and around the box. Ozil can't find a way through, Alexis can't find a way through. Welbeck can't find a way through. Bellerin just doesn't have the space to run into.
90+2' Ramseyyyy... OVER THE BAR! Ozil's pass to Ramsey in the box is perfect but his first-time shot is tired and off target - much to De Gea's relief.
87' YELLOW CARD! A hopeful long ball up field sees Lukaku and Koscielny wrestle for the ball and it's the Belgian who wins the decision. Mourinho wants Koscielny sent off for a last-man challenge but Bellerin was tracking back.
83' Welbeck's shot is deflected and De Gea goes for the safe option and sends it over the bar. It was looping in and dipping and the goalkeeper was not taking any chances.
80' It's 'Park the Bus' time for United with 7 players in the box. You can't blame them. They're down to 10 men and have a two-goal lead to protect with 10 minutes to go.
76' SUBSTITUTION: Sead Kolasinac makes way for Olivier Giroud! This is going to be attack vs defence with Giroud, Lacazette and Welbeck on alongside Iwobi, Alexis and Ozil!
74' RED CARD! Paul Pogba is sent off for a cynical stamp on Bellerin! The Spaniard was attempting to block a dribble but Pogba's foot lands on the back of Bellerin's leg and the referee has no qualms about sending him off.
72' YELLOW CARD: Bellerin's challenge on Ashley Young to stop a United counter is punished by the referee. He won't complain - one for the team and all that.
71' Corner for Arsenal! Koscielny (!) makes a run into the box to receive a pass from Bellerin and his cross (just before it goes out of play) is cleared by Rojo for a corner. But yet again Arsenal fail to make good use of the set-piece.
68' Arsenal's buildup is patient and they're waiting for the right pass before making a decision. But United's defence has dropped deep and stood firm to weather the onslaught - ever ready to launch a counter-attack through Lingard.
63' It's another Man Utd counter-attack! Koscielny is beaten by Pogba's trickery and the French midfielder lays it on a plate for Jesse Lingard who taps it in with absolutely nobody to challenge him.
61' Matic looks good to continue and he is back on the pitch. But United are resorting to time-wasting tactics and the home crowd are letting them know exactly what they think of it. United just want some time to catch a breath but Arsenal are in no mood to give them any respite.
We're not done yet though. You can follow Athletic Bilbao vs Real Madrid live which kicks off at 1:15 AM IST.