The ex-Arsenal player hit the victor to finish a noteworthy rebound after Galatasaray had started to lead the pack.
With the tie ready at 0-0 after the principal leg, Brazilian protector Marcao gave the hosts the lead before Pedri adjusted with a fine individual objective.
Aubameyang's 49th-minute victor sent Barca into Friday's quarter-last draw.
Barca ran down the clock, chafing the home group who began tossing containers and plastic cups onto the field and the ref halted the game for a couple of moments while the Galatasaray players attempted to quiet things down.
Aubameyang, 32, joined Barcelona on a free exchange in February following four years at Arsenal and the Gabon forward has been a great marking.
Xavi's side had dropped into the Europa League subsequent to completing third during the gathering phase of the Champions League, behind Bayern Munich and Benfica.
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