The result lifted Les Verts - already assured a Europa League spot thanks to the League Cup title they clinched last Saturday - up to fourth on 57 points, two behind third-placed rivals Olympique Lyon, whom they face away on Sunday.
The top two teams in Ligue 1 qualify directly for Europe's premium club competition with the third-placed side facing a playoff.
At their Stade Geoffroy Guichard, St Etienne fell behind after 15 minutes.
Former Chelsea forward Adrian Mutu collected a Benjamin Andre cross in the box and his deflected low shot beat Stephane Ruffier.
St Etienne, however, hit back eight minutes later through Aubameyang as the Gabon striker tapped in from a Yohann Mollo cross.
Mollo then released Mathieu Bodmer, whose attempt on the turn went just past Guillermo Ochoa in the 58th minute.
Two minutes later, Renaud Cohade fired past Ochoa after being set up by Brandao's clever back heel.
In the 76th minute, Mutu pulled one back by converting a penalty following a foul on Dennis Oliech by Loic Perrin, only for Aubameyang to put the result beyond doubt late on with a low shot which took his tally to 19 league goals this season.
Bottom club Troyes kept their slim hopes of staying in the top flight alive when goals by Jean-Christophe Bahebeck and Jeremie Brechet earned them a 2-1 win at Stade Rennes, who were beaten by St Etienne in the League Cup final last Saturday.
Rennes, whose coach Frederic Antonetti announced on Tuesday that he would leave at the end of the season, reduced the arrears through Julien Feret's penalty but it did not prevent them from losing their sixth game in a row in all competitions.
Troyes remain at the bottom of the standings with 28 points, six points from safety with five games left, while Rennes stay 10th on 42.