Riccardo Calafiori scored the only goal after the Italian defender pounced on a huge mistake by United’s stand-in goalkeeper Altay Bayindir.
United have splashed out £200 million on new forwards to remedy a lack of punch in the final third.
Despite promising debuts, Matheus Cunha and Bryan Mbeumo failed to find the net, while substitute Benjamin Sesko could not make Arsenal pay for not pursuing their interest in the Slovenian.
After finishing second for the past three seasons, the pressure is on Arsenal boss Mikel Arteta to deliver the club’s first league title since 2003/04.
The Spaniard was left to depend on his reliable defence and goalkeeper David Raya to secure a huge three points as the visitors never got going as an attacking force.
Only four other teams scored fewer than United’s 44 goals in 38 Premier League games last season as the English giants endured their worst campaign for 51 years, finishing 15th in the table.
The new arrivals have at least lifted the mood around Old Trafford and the majority of the 75,000 fans in attendance could at least leave encouraged by the performance of Ruben Amorim’s men.
Cunha and Mbeumo unsettled Arsenal’s normally unflappable centre-back pairing of Gabriel Magalhaes and William Saliba early on.
However, United’s good work was undone by a glaring error from Bayindir, who was deputising for the injured Andre Onana.
The Turkish international meekly flapped at an inswinging Declan Rice corner on 13 minutes, allowing Calafiori the simplest of tasks to head into an unguarded net.
Patrick Dorgu came closest to a United reply before half-time with a powerful effort from distance that came back off the post.
Mbeumo and Cunha saw tame efforts easily saved by Raya, while the Spaniard did brilliantly to divert another Cunha shot across the face of goal.
Arsenal had held interest in Sesko for well over a year before instead pursuing a move for Viktor Gyokeres as the solution to their need for a number nine.
The Swede had a quiet Premier League debut and was replaced before the hour mark by Kai Havertz.
Sesko made his entrance moments later to a hero’s welcome after rejecting the advances of Newcastle for the lure of the 20-time English champions.
United continued to enjoy the better of the play without finding the finish as Mbeumo saw a powerful header expertly clawed out by Raya.
But Arsenal held firm to keep pace with title rivals Liverpool and Manchester City, who also won on the opening weekend of the campaign. (AFP)