Victory has taken the Gunners up to eighth on the table while United wallow in lowly 15th on just seven points from six games.
The first real chance of the game fell the way of Mason Greenwood in the 21st minute after Marcus Rashford played his England colleague through but Bernd Leno in the Arsenal goal was on hand to keep out the 19-year-old’s effort with his foot.
Willian came close to scoring his first Arsenal goal since his summer move from Chelsea in the 38th minute after a neat one-two with Aubameyang but the Brazilian’s effort clipped the top of the cross bar and went over.
Another slick Arsenal move ended up with Bukayo Saka heading Hector Bellerin’s cross just over the bar two minutes before the break.
Back from recess, Thomas Partey tested David De Gea from range in 58th minute as Arsenal threatened to score.
The game’s defining moment came in the 69th minute when Paul Pogba clipped Bellerin in the penalty box, and Aubameyang, without a Premier League goal since the opening day of the season, stepped up to send De Gea the wrong way for the only goal of the game.
United came close to equalizing in the 84th minute when substitute Donny Van De Beek’s cross was turned onto the upright by Mohamed Elneny.