Aubameyang gave the Gunners the lead after just six minutes, squeezing an effort past Nick Pope to get his side off to a perfect start.
Bernd Leno and Granit Xhaka were both at fault as Chris Wood equalised towards the end of the first-half with both sides creating chances to win the game in the second period.
Arsenal were left furious as VAR refused to award them a penalty after a handball incident involving Nicolas Pepe and Erik Pieters and were unlucky again in injury time as Dani Ceballos struck the post with a well hit effort.
The Gunners head to Olympiacos for the first leg of their Europa League last 16 tie on Thursday before a huge north London derby at home to Tottenham and Sunday.
Writing on Twitter after the game, Aubameyang admitted his side created more than enough to seal all three points at Turf Moor and were guilty of failing to take their chances.
But with the big games coming thick and fast, the striker urged his side not to dwell on the result and look forward.
Arsenal could be seven points behind arch-rivals Spurs by the time they meet next weekend.
Jose Mourinho’s side host Crystal Palace on Sunday.