Just hours after being named the Premier League 2 Player of the Month for August, the 17-year-old struck his sixth goal of the season, finding the top corner on 33 minutes.
Within five minutes Arsenal were 2-0 up, this time Josh Da Silva also scoring from a free-kick.
In wet conditions, United, for whom Luke Shaw played in central defence, could not find a way back in the game at Leigh Sports Village Stadium.
United, who are eighth, next travel to Chelsea on Monday 18 September. Second-placed Arsenal host Leicester City next Friday.
See: Man Utd report