Shortly after David De Gea's double save denied Arsenal duo Bukayo Saka and Matteo Guendouzi, Scott McTominay's superb 45th-minute shot from the edge of the area gave Man Utd the lead.
McTominay sent a free header over the bar from a corner before Arsenal equalised on 58 minutes.
Aubameyang dinked the ball over De Gea from Saka's pass and, although he was initially deemed offside, the decision was overturned by the Video Assistant Referee (VAR) review.
Moments later Saka's close-range shot was deflected over by Victor Lindelof while, at the other end, Paul Pogba's curling shot fizzed narrowly wide and Marcus Rashford's stoppage-time free-kick was pushed out by Arsenal goalkeeper Bernd Leno.
Man Utd drop down to 10th with nine points. Arsenal lie fourth with 12.
Man Utd: 6 Oct v Newcastle (A)
Arsenal: 6 Oct v AFC Bournemouth (H)