Jan Vertonghen conceded a penalty with a handball to enable Aubameyang to slot in the opener on 10 minutes.
But Spurs struck twice in four minutes to lead at half-time. Eric Dier glanced in Christian Eriksen's free-kick before Harry Kane scored a penalty after Rob Holding's foul on Son Heung-min.
After the break, Aubameyang brilliantly swept in a long-range equaliser, taking his tally to 10 PL goals this season.
Substitute Alexandre Lacazette put Arsenal ahead with a deflected effort on 74 minutes, and that was swiftly followed by Lucas Torreira’s drive from an acute angle to make it 4-2, his first goal for the club.
Vertonghen was sent off late on as Unai Emery’s side move above Spurs on goal difference to fourth on 30 points.
Arsenal: 5 Dec v Man Utd (A)
Spurs: 5 Dec v Southampton (H)