Unai Emery's men came into this match looking to get back to winning ways after two consecutive defeats had ended their 22-match unbeaten run, while the visitors were looking to build upon an impressive performance in last weekend's 1-0 defeat at Tottenham.
Emery handed Mesut Ozil the captaincy and the German appeared to take inspiration from the armband as he helped set up the opening goal with a sublime pass. Ozil spotted Sead Kolasinac running towards the back post and played the ball perfectly into his path.
The Bosnia and Herzegovina international flicked the ball back to Aubameyang, who found the bottom corner for his 11th Premier League goal of the season to give Arsenal a 13th minute lead.
Tempers threatened to boil over 10 minutes before half-time with Ashley Barnes and Sokratis Papastathopoulos wrestling each other to the ground -- an incident which saw the Burnley man booked by referee Kevin Friend.
But, despite leading at half-time for the first time this season, it was not all good news for Arsenal as their injury crisis worsened with Nacho Monreal forced off on 37 minutes and replaced by Stephan Lichtsteiner.
Arsenal seemed to have put the result to bed just three minutes after the break when Aubameyang fired past Joe Hart to go above Mohamed Salah as the outright Premier League top scorer with 12.
However, they were pegged back on 62 minutes after their defence failed to clear the ball and Barnes drilled a shot into the corner.
Following the goal, Arsenal looked rattled and the Burnley forward players looked to enter the home side's box much more frequently. Barnes was fuming when he was adjudged to have committed a foul after working his way into the six-yard box.
Burnley boss Sean Dyche then took the unusual decision to replace his to forward for different pair of strikers as Barnes and Chris Wood came off for Sam Vokes and Matej Vydra as he looked to make it 2-2-.
But, just after the referee's decision to add five minutes of stoppage time had created a nervous energy around the stadium. Alex Iwobi made the game safe with a late third.
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