The Dutch striker needed fewer than three minutes to put United in front before Patrice Evra doubled their lead in the 67th minute.
Arsenal, for whom this defeat was their third in five matches, then saw this latest loss made worse when midfielder Jack Wilshere, in only his second game back following a long injury lay-off, was sent off for a second bookable offence after he caught Evra on the ankle.
Cazorla pulled a goal back for Arsenal deep into stoppage time with virtually the last kick of the match, but defeat meant the Gunners were left nine points off the summit just 10 games into the season
