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.
59' Play is stopped after a clash of heads. Matic clears the ball half a second before Koscielny's head makes contact with Matic. The Arsenal captain walks away shaking his head but Matic needs treatment.
58' YELLOW CARD: Rojo is booked for stepping on Alexis Sanchez's heel. The Chilean is still wincing in pain as Arsenal win a free-kick near the corner flag.
56' SAVE! De Gea is on hand yet again to deny Lacazette from point-blank range. The Frenchman received the ball outside the six-yard box and fired a left-footed shot that should have made it 2-2.
54' Corner for Arsenal. They're growing into the game and Iwobi gets a shot off that is deflected over the goal for a corner. But the ever-present Pogba is able to clear with a strong header.
52' CLANG! United's turn to miss! Lingard is through on goal but his shot rebounds off the far post. Martial gets on the rebound and his shot is blocked by Monreal who puts his body on the line.
Just moments later, Iwobi tests De Gea at the other end with a shot that stings his gloves!
48' United went to sleep! A lob over the defence finds Aaron Ramsey free but his trap falls backward - but wait! Alexandre Lacazette is on hand to fire it home. Both players were behind the United defence but Ramsey was onside and Lacazette certainly was!
47' Manchester United are in no hurry to attack. They're happy to sit back in a 4-5-1 formation when they don't have the ball, allowing Arsenal to dictate the pace of the game.
Phew! What a half! Two counter-attacking goals in the first 11 minutes are the difference between the two sides. Arsenal have dominated possession but have failed to breach the wall that is David De Gea in the United goal.
De Gea makes a save at the far post to prevent a Lukaku own goal and Koscielny holds on to the ball for what seems like ages as United defenders don't go in in fear of conceding a penalty. When he eventually gets rid of it, Arsenal fail to take advantage.
45+1' Matic fouls Lacazette and the Arsenal players surround the referee. No booking as the fans around the stadium boo. But the Gunners have a free-kick out on the left.
44' Bellerinnn... SAVED! An Arsenal attack sees some more great passing before Bellerin finds space to let fly a rocket on goal that is palmed away by De Gea! Moments later it's Kolasinac who tries his luck and De Gea makes another save.
42' A promising attack from Arsenal sees Lacazette, Alexis and Ramsey combine with some slick passing and great chest control by Alexis. They win a corner and the resulting set-piece sees the ball fall kindly to Ramsey. But Matic is on hand to block his effort on goal!
40' Xhaka cleans out Martial with a tackle but the referee doesn't even bother blowing the whistle as Xhaka got the ball first and it was his momentum that took Martial out.
38' Bellerin is whistled for a foul after he nudges Young off the ball. He had been released by Iwobi but the referee gives the decision to United. Was that really a foul? It looked a bit physical but is usually not given by refs in the Premier League.
36' Ozillll... SAVED! Lacazette finds Ozil free as a bird on the edge of the box and his lateral pass is taken first time by the German. But his low shot is straight at De Gea who catches the ball with ease.
34' SAVE! A United counter-attack sees Pogba drift wide before crossing the ball to the centre. Kolasinac makes a mess of the clearance and Lukaku almost fires home before Cech pounces on the ball and holds on to it for dear life.
Lacazette receives the ball inside the six-yard box after Rojo messes up on the clearance. The Frenchman dances his way past everyone and takes his time before he fires a shot which is deflected by De Gea on to the bar. That could easily have been 1-2! Great save!
30' It's Ozil who takes the free-kick and the German lobs it over the wall towards the near post but Young has read it perfectly, leaving the wall and sprinting back to head it away. De Gea will buy him a drink after that. Superb anticipation!
29' Free-kick for Arsenal! Alexis wins another free-kick as Rojo's careless tackle brings him down right on the edge of the box. This time it's in Ozil territory out on the right - ideal for a left-footed player to shoot.
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