A turgid first half in front of 2000 fans saw Alexandre Lacazette have the only shot on target but the game livened up when Xhaka was dismissed for a needless grapple with Ashley Westwood.
The Burnley midfielder was then on hand to send in a corner which Aubameyang, without a goal from open play for Arsenal since the opening weekend of the season, headed to beat his own goalkeeper and settle the game.
This is the first time in over 60 years that Arsenal have lost four home league games in a row and the result saw Sean Dyche’s men end a six-match losing streak at the Emirates.
Burnley wasted a fine opportunity to open the scoring and further rock the confidence of the Arsenal side.
Robbie Brady was in space down the right and a fine cross found Chris Wood free in front of goal but the New Zealand international could only head wide when he should have scored.
Rob Holding and Lacazette came close for the hosts, the latter denied by a fine Nick Pope save as he got onto the end of a Kieran Tierney cross.
That would be the only shot on target in a dull first half, with Arsenal seemingly given a rocket in the dressing room at half-time.
Tierney, Aubameyang and Bukayo Saka drew saves from Pope before Xhaka’s moment of madness saw him sent off just before the hour.
After an altercation with Dwight McNeil following a Xhaka foul, the Switzerland midfielder tangled with Westwood, initially picking up a booking from referee Graham Scott.
Scott was then called over to check the pitchside monitor and upgraded the punishment when it became clear Xhaka had grabbed Westwood by the throat.
The red card seemed to spur Arsenal on somewhat and they continued with a similar pattern of play as Dani Ceballos replaced the ineffectual Lacazette.
But they would go behind from a corner, with Mohamed Elneny booked for wrestling James Tarkowski to the ground before the set-piece, when it was eventually swung into the near post, Aubameyang could only get his head to the ball and turn it into his own net.
Arsenal would rally with 10 men and pushed forward in the hope of an equaliser, even Bernd Leno going up for a last-minute corner which was cleared off the line.
The full-time whistle would be met with jeers from the returning fans as Arsenal lost a fourth straight home league game for the first time in over 60 years.