The result lifted the Gunners two places up to fourth on 66 points from 33 games, ahead of fifth-placed Chelsea on goal difference and two in front of sixth-placed Manchester United. Watford stayed 10th with 46 points.
The fast-paced clash took a decisive turn in a frantic one-minute spell early on, as Aubameyang found the back of the net in unlikely fashion before Watford striker Troy Deeney was shown a straight red card for elbowing Lucas Torreira.
Despite their numerical disadvantage, Watford kept pressing and missed a string of chances to draw level, having twice been denied by the woodwork as well as by some good saves from Arsenal keeper Bernd Leno.
Aubameyang, Alex Iwobi and Henrikh Mkhitaryan also came close at the other end but Arsenal were forced to hang on in the closing stages with Watford throwing men forward.