A second-half penalty from captain Pierre-Emerick Aubameyang gave us a richly-deserved three points at Old Trafford - our first Premier League win there for 14 years.
We were the more positive side right from the opening exchanges, snapping into tackles and closing down well, and much of the opening quarter of an hour was played in the United half.
Our first sight of goal came when the overlapping Hector Bellerin fizzed a low ball across goal, but it was just ahead of the sliding Pierre-Emerick Aubameyang at the far post.
Despite our superiority in terms of possession, it was United who had the first shot on target when Mason Greenwood ghosted in at the far post to draw a smart low save from Bernd Leno.
We kept driving forward. Alexandre Lacazette had the ball nicked off his toes inside the area when he was about to pull the trigger while Willian fired against the bar after a neat one two with Aubameyang.
But the best chance of the half came late on. Bukayo Saka then headed over from a glorious position in front of goal, set up by Bellerin's pinpoint cross.
Aubameyang sent a shot just wide at the start of the second half before Thomas Partey brought a save from David De Gea with a fierce drive.
We certainly deserved the lead when it came. We had been knocking at the door and finally went ahead from the penalty spot. Bellerin was brought down in the area by Paul Pogba and Aubameyang strode up to tuck home from 12 yards and end a personal five-game scoreless run in the Premier League.
We came under much more pressure in the final ten minutes and United hit the post late on when a Donny van de Beek shot cannoned off Mohamed Elneny and then the upright.
But hang on we did, to record our first Premier League win at Old Trafford since 2006.
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Enjoy match highlights, training and behind the scenes to get closer to the likes of Pierre-Emerick Aubameyang, David Luiz, Vivianne Miedema, Nicolas Pepe, Alexandre Lacazette, Leah Williamson, Mesut Ozil, Bernd Leno, Danielle van de Donk, Willian, Hector Bellerin, Jordan Nobbs, Bukayo Saka, Kim Little, Gabriel Martinelli, Thomas Partey and more.
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Arsenal Football Club were formed in 1886 and amassed 13 League titles, 14 FA Cups. Some of their greatest players include: Thierry Henry, Dennis Bergkamp, Tony Adams, Ian Wright, Robert Pires, Liam Brady, Patrick Vieira, Cliff Bastin and Charlie George.