Mikel Arteta will not be particularly pleased with the performance, as the Gunners struggled at both ends of the pitch for large periods, yet they were typically resilient to keep the hosts at bay.
Improvements will be needed in the coming weeks and months, but it is a positive sign in itself that Arsenal can struggle to that extent and still win.
Here are three things we learned at Old Trafford…
Debut: Viktor Gyokeres
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Gyokeres fails to make impact
Viktor Gyokeres could very easily have been lining up here in a United shirt.
Ruben Amorim was keen to bring the striker, who he worked with at Sporting, to Old Trafford this summer but it was Arsenal who won that particular race.
There was very little for Gyokeres to work with in the first half of his Premier League debut. He held the ball up well as Matthijs de Ligt stuck close to him, proving too strong for the centre-back on more than one occasion.
Gyokeres got back behind the ball in Arsenal’s defensive shape but that limited his impact in attack. He was jogging by the halfway line during one counter as Odegaard drove at the United defence.
On the couple of occasions Gyokeres did get in behind, his delivery from the byline was poor.
His best opening came shortly after the break when he drifted out to the left and was played in on the counter, but Gyokeres tripped over on the hour mark and then hauled Casemiro down.
Replaced on the hour mark by Kai Havertz, this was not the debut Gyokeres would have dreamt about last night.
Struggles: William Saliba
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Gunners shaky in defence… but find a way
Arsenal’s title challenges in recent seasons have been built on a rock-solid defence and clean sheets. They had only one of those here.
Particularly in the first half, the Gunners were a mile away from the standards they have set in previous campaigns.
Saliba let a couple of balls over the top bounce early on, nearly letting Mbeumo in, and that set the tone for a nervy performance.
They were unusually vulnerable on the counter, United’s players keeping their width and leaving the likes of Riccardo Calafiori and William Saliba badly exposed at times. Matheus Cunha and Bryan Mbeumo both had plenty of joy.
The quick switch out wide was on every time for United and Patrick Dorgu very nearly equalised from one such break, his effort beating David Raya but flicking off the outside of the post.
It was not quite so open after the break, though there were still a number of ragged clearances from Arsenal defenders that kept United on the attack.
Gabriel and Saliba looked more confident when the defending was last-ditch in their own box, throwing their bodies in the way, but there was none of the usual control.
Arsenal found a way and to do so at Old Trafford, regardless of where United are as a side, is impressive. However, a more efficient team on the counter would surely have made the Gunners pay.
Options: Noni Madueke
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Beyond the result, it was not an afternoon for great positives for Arsenal but the team sheet offered one ahead of the match.
For much of last season, there was little in the way of options for Arteta to turn to off the bench, the Arsenal boss at turn having to use Kieran Tierney as a winger.
Here, though, he could turn around on the touchline and see Noni Madueke, Havertz, Ethan Nwaneri and Leandro Trossard waiting in reserve.
Max Dowman, the 15-year-old who has shone in pre-season, travelled with the squad but was not named on the bench.
Madueke and Havertz both came on and the German in particular impressed in his cameo, holding the ball up well and having more effective moments in the final third than Gyokeres.
Arteta also had the luxury of changing both full-backs as they tired and there was no drop in quality, with Jurrien Timber and Myles Lewis-Skelly introduced for the final 20 minutes.
Arsenal fans will be hoping for more business before the end of the window, particularly on the left wing, but there is a strong feel to the squad at the start of the season.