The Gabon forward punished Leeds goalkeeper Illan Meslier by finding space to fire in at the near post 13 minutes in to lift Mikel Arteta early on following a poor run of results.
Arsenal were awarded a penalty later in the half as Bukayo Saka went down under pressure from Liam Cooper, but referee Stuart Atwell changed his original decision after watching the replay on the VAR pitchside monitor.
However, Arsenal did soon have a spot-kick as Meslier lost possession cheaply in his own box and brought down Saka, with Aubameyang making no mistake from 12 yards.
Hector Bellerin then beat Meslier at his near post on the stroke of half-time to cap a miserable opening 45 minutes for the Leeds keeper, with Arsenal taking full advantage.
The punishment continued soon after the break as half-time sub Helder Costa was caught on the ball, and Aubameyang completed his hat-trick by heading home a smart Emile Smith Rowe cross.
Leeds pulled a goal back through a bullet header from Pascal Struijk and then set Arsenal nerves jangling as Helder Costa halved the deficit with 20 minutes remaining, but Arsenal saw things out to collect a much-needed three points.