Pierre Emerick-Aubameyang's penalty was the difference at Old Trafford but who starred and who struggled for Manchester United and Arsenal?
David de Gea - 5
Communication mix-up with Harry Maguire in the opening minutes might have been costly but as impressive as Arsenal were in the first half, had little to do. Gathered Partey's fierce drive comfortably enough after the break but beaten from the spot once again.
Aaron Wan Bissaka - 4
No easy task dealing with the quick feet of Bukayo Saka, bundling the youngster over early in the game after a mistake in possession. But repeated errant positioning might have cost his side; lost Aubameyang several times in the first half and allowed Saka a free header just before the break.
Victor Lindelof - 6
Several key interventions - including an important toe to deny Aubameyang towards the end of the first half, then another to thwart Lacazette, though almost punished when Willian hit the crossbar.
Harry Maguire - 6
Some important headed clearances and tried to stretch the pitch with a couple of driving diagonals looking for Bruno Fernandes. Caught between nodding back across goal and seeking the top corner when Shaw delivered a delicious ball but won most of his duels.
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Luke Shaw - 6
Solid enough but striking contrast in first half between positions of him and Wan-Bissaka - and those of Kieran Tierney and Hector Bellerin. Higher up pitch after break and glorious whipped ball early in the second half should have been converted by Maguire.
Fred - 4
So impressive in midweek but loose in possession and clumsy in the challenge. Deployed in holding role but a nervy watch for United fans after picking up a booking for a challenge on Willian. Taken off just after the hour mark for Nemanja Matic.
Scott McTominay - 5
Struggled in the first half in diamond shape lauded after that RB Leipzig rout as he drifted too often into Fred's space. "He's the awkward bit of the diamond," said Gary Neville in the first half. "He's not where he needs to be to create space for others. He's playing too deep. The balance with him and Wan-Bissaka is not quite right." Stayed on to help stave off the Arsenal counter-attack.
Paul Pogba - 4
Like fellow United midfielders, bossed by Thomas Partey in the first half at Old Trafford, though made important defensive intervention at the near post from Willian's wicked free-kick. Struggled in transition and frequently dispossessed, then naively clipped Bellerin after getting on the wrong side to concede the penalty that Pierre-Emerick Aubameyang dispatched. Infuriating again.
Bruno Fernandes - 4
Tried to orchestrate but, like several of his team-mates, too often loose in possession in the first half. Moved to the No 10 position after the break but struggled to spark Solskjaer's side and was replaced by Donny van de Beek with 15 minutes to play. Really ineffectual.
Marcus Rashford - 5
Looked sharp enough in the first half - played a glorious curling ball into Mason Greenwood's path - despite little service. Let-off after loose header from a throw-in let in Aubameyang. Too peripheral overall. Roy Keane described his body language as "shocking".
Mason Greenwood - 5
Had United's only shot of the first half - they last had fewer in the opening 45 minutes when they had none against Manchester City in October 2015 - but though anticipated Rashford's pass, drilled straight at Leno from a tight angle. Over-zealous challenge on Lacazette in the second half earned him a booking and taken off.
Nemanja Matic - 6
Replaced Fred just after the hour and tried to exert influence. Thought he deserved a penalty after a clever give-and-go with Van de Beek and kept Leno alert with a low drive late on.
Edinson Cavani - 5
Replaced Mason Greenwood in the 74th minute. Willing but not match fit and found himself having to drift out left to get on the ball. Booked in injury-time for a challenge on Gabriel.
Donny van de Beek - 7
On for Fernandes in the 75th minute but looked sharp and incisive in limited minutes; enough promise to boost his rating here. Showed neat feet and pacy centre was almost diverted into his own net by Elneny.
Bernd Leno - 7
Hardly tested as Arsenal dominated the game, but he did have to be alert to keep out Greenwood's powerful low drive with his feet at his near post in the first half. Unlike in his last few games, he was solid with the ball at his feet and went long at all the right times. Had a bit of luck late on when Elneny's attempted clearance hit him in the face and the ball rebounded onto the post But when it's your day, it's your day.
Rob Holding - 8
On his return from a hamstring injury, the 25-year-old had the tough prospect of dealing with man of the moment Marcus Rashford. His task was made harder because of an early booking for a foul on the United forward, but he coped well. He was strong in the tackle and dominant in the air, plus he was very neat and tidy on the ball as Arsenal played out from the back.
Gabriel Magalhaes - 9
Rock solid at the heart of the Arsenal defence. He also had to contend with an early booking for a foul on Rashford, but he was always in the right place at the right time for the Gunners. He repelled everything that was sent his way and made a decisive tackle late on to deny Matic in the penalty area. A key component of the new spine being built at Arsenal by Arteta.
Kieran Tierney - 7
The last piece of Arsenal's three-man defence, and again, the Scot did not put a foot wrong. He will not take the plaudits of Gabriel or Holding, but he certainly played his part in what was an excellent defensive performance from the Gunners.
Hector Bellerin - 8
An impressive performance from the Spaniard. He popped up infield on numerous occasions to cause United plenty of problems. He ably supported Willian in attack and Holding in defence, and his service into the penalty area was excellent. Played a crucial role in Aubameyang's winning goal, drawing the foul to win the penalty from Pogba.
Mohamed Elneny - 8
A surprise inclusion from Arteta with Granit Xhaka left on the bench. However, the Egyptian produced a solid display for his side. He did plenty of dirty work, screening Arsenal's defence alongside Thomas Partey. He played the simple pass all afternoon and drove forward whenever given the opportunity. Alongside Partey, they dominated the midfield area, which played a key part in the Gunners' victory. Rode his luck with a late block but the ball was on Arsenal's side as it hit Leno in the face before rebounding off the post.
Thomas Partey - 9
Showed exactly why Arsenal paid the £45m required to sign him on Deadline Day from Atletico Madrid. A huge presence for the Gunners alongside Elneny, who he struck up an excellent partnership with. Another key component of Arsenal's new spine and Arteta will be hoping to see much more of that in the coming weeks and months. Top for Arsenal touches, possession won, tackles and interceptions and dribbles completed. "He's a midfielder player who can do everything," said Jamie Redknapp.
Bukayo Saka - 7
Another decent showing from the England international. In tandem with Tierney and Aubameyang down the left, he was always looking to influence the game in a positive way and that trio gave Wan-Bissaka a difficult afternoon. However, he will know he should have done better when heading over when presented with a golden opportunity to score from eight yards.
Willian - 7
Lost possession a number of times early in the game, but he was always trying to move Arsenal forward. He was always asking for the ball and supported by Bellerin, they gave Arsenal an excellent outlet down the right. He was inches away from a goal when his strike clipped the top of the crossbar.
Alexandre Lacazette - 8
Nothing in the stats column in terms of goals or assists, but the Frenchman contributed in plenty of other ways for his side at Old Trafford. He worked tirelessly for his side, leading Arsenal's excellent press from the front. He put United's defenders under huge pressure when they had the ball and it was a key part of the Gunners' game plan as Solskjaer's side struggled to get past the press all game. He also used his strength well to hold the ball up for his side and brought his team-mates into the game whenever he had the chance.
Pierre-Emerick Aubameyang - 7
Arsenal could not get their main man involved enough from the left in the first half. He could have had a tap in had he anticipated Bellerin's cross earlier and he should have done better early in the second half when played in by Lacazette. But when it mattered, the Arsenal skipper delivered, converting from the spot to seal all three points. It was a goal he desperately needed too having gone five games without a goal in the league.
Eddie Nketiah - 6
Run his socks off for the cause in the final few moments to help get his side over the line. He made a good contribution late on with an excellent forward run, which allowed him to take the ball into the corner to waste a valuable few seconds.
Ainsley Maitland-Niles and Shkodran Mustafi - n/a
Brought on in the final minutes to help the defensive cause and they did their jobs as Arsenal held on for a crucial victory.
Manchester United go to Istanbul Buyuksehir in the Champions League at 5.55pm on Wednesday, before going to Everton at 12.30pm in the Premier League on Saturday.
Arsenal host Molde in the Europa League on Thursday at 8pm, and then welcome Aston Villa to the Emirates at 7.15pm on Sunday, live on Sky Sports Box Office.