Arsenal defender Riccardo Calafiori nodded in from close range in the 13th minute after United back-up goalkeeper Altay Bayındır, who started ahead of Andre Onana, flapped at the ball from a corner whipped in by Declan Rice.
While Arsenal followed likely title rivals Liverpool and Manchester City in claiming an opening-weekend victory, United fell to a loss that is all too familiar under Ruben Amorim following a woeful 15th-place finish last season by English soccer's fallen giants.
United spent around $A416 million on revamping their attack in the offseason, with Bryan Mbeumo and Matheus Cunha starting the match and Benjamin Sesko coming off the bench in the second half.
While the team played with a good intensity at Old Trafford, Arsenal's strong defence stood firm.
At the other end, Viktor Gyokeres endured a difficult first competitive start for Arsenal, whose goal came from a familiar route with Mikel Arteta's team so imposing from set-piece situations in recent seasons
Chelsea made an underwhelming start as Crystal Palace ground out a goalless draw at Stamford Bridge.
After a truncated pre-season following victory in the Club World Cup, everything pointed to a Chelsea side lacking both preparation and rest as Oliver Glasner's team coped relative easily with a new-look yet disjointed attack.
Eberechi Eze started for Palace despite speculation he is about to leave and, if there were doubts about how supporters felt about the player whose goal won them the FA Cup in May, they were dispelled when he was substituted to a standing ovation late on.
The England international provided the game with its only major talking point, lashing in a brilliant free-kick in the first half that was ruled out after Marc Guehi obstructed Chelsea's wall, drawing a furious response from Palace fans.
Chelsea were playing 35 days after their win over Paris St Germain in the Club World Cup final in the United States and showed signs of mental fatigue in a match generally low on creativity.
Nottingham Forest made a mockery of Nuno Espirito Santo's pre-match worries as they beat Brentford 3-1.
Nuno expressed his "concern" for the campaign ahead of the match, citing a lack of options in his squad, but he will feel better after watching a rampant display at the City Ground.
After new signings Omari Hutchinson and James McAtee were unveiled before kick-off, their new team-mates put on a show as Chris Wood's double and a debut goal for Dan Ndoye put them 3-0 up at the break.
Igor Thiago got the Brentford on the scoresheet with a second-half penalty but there was nothing to threaten Forest's winning start.
