Three days after netting a hat trick against Valencia to send Arsenal through to the Europa League final against Chelsea, Aubameyang scored in the 52nd and 63rd minutes to take his league tally for the season to 22, along with Liverpool duo Mohamed Salah and Sadio Mane.
Ashley Barnes reduced the arrears at Turf Moor just two minutes after Aubameyang's second but a last-gasp Eddie Nketiah goal secured Arsenal the three points, which were only enough for fifth place with fourth-place Tottenham drawing against Everton.
Arsenal boss Unai Emery knew the Europa League represents a much better chance to clinch Champions League football for next season and only Aubameyang and Nacho Monreal stayed in the starting lineup from Thursday night.
Burnley has been uncharacteristically sloppy at the back this season and it was another poor error that presented the opener to Aubameyang. Jack Cork misjudged a pass back to Ben Mee, the ball skipped off his toe straight to the Arsenal striker and he gave Burnley goalkeeper Thomas Heaton no chance with a cool finish.
Aubameyang made it six goals in eight days and 31 for the season by thumping in Alex Iwobi's cross to double the lead. Burnley finished 15th.
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