Carlo Ancelotti's men roared away from the pack by winning their opening five league games and outscoring some of the lesser lights in the division 21-1 but stumbled when they came up against their first major obstacle at Eastlands.
Arsenal also lost their unbeaten league record last week when they were surprisingly beaten 3-2 at home by West Bromwich Allbion.
City outmuscled Chelsea in midfield with their powerful Dutchman Nigel de Jong giving a robust performance, but Arsenal's injury-prone and less robust players will have to chose another route.
Goalkeeper Manuel Almunia had a poor game and injured himself saving a penalty he conceded. The often-criticised Lukasz Fabianski replaced him for Tuesday's Champions League match against Partizan Belgrade and impressed, but he is always capable of a major gaffe.
The 25-year-old Polish international said: "I have never been bothered by the things said about me, I am always trying to focus on my job and my work. Now I am ready to play against Chelsea, so we will see if I do."
United's 1-0 win at Valencia in the Champions League on Wednesday will have boosted their self-belief after their 2-2 draw at Bolton Wanderers last week and they face a tricky visit to Sunderland, managed by their old player Steve Bruce, on Saturday.
Striker Wayne Rooney will be missing with an ankle injury, but the match could mark Rio Ferdinand's return to league action after he returned to the side on Wednesday for his second Champions League apppearance of the season after having missed the start of the league campaign through injury.
