Mikel Arteta's side, which had an 85th-minute penalty taken away after a VAR (video assistant referee) review, faces a two-legged UEFA Europa League Round of 16 showdown with Olympiacos either side of next Monday's (AEDT) north London derby with Tottenham Hotspur.
It will tackle that run of games knowing its top-four hopes are all but gone, with silverware and local bragging rights providing the primary motivation.
Pierre-Emerick Aubameyang, whose own goal handed Burnley a 1-0 win over 10-man Arsenal at Emirates Stadium in December, capitalised on some slack defending to put the visitors ahead after just six minutes at Turf Moor.
Burnley drew level in fortuitous circumstances before half-time, Xhaka – the man sent off in the reverse fixture – attempting a pass inside his own area that hit Chris Wood's hip and flew in.
It was punishment for the Gunners' profligacy, with Aubameyang and Bukayo Saka having missed chances to increase their lead.
Arteta was left to reflect on two points dropped after referee Andre Marriner had to reverse the decision to award a late penalty when Erik Pieters brilliantly kept out Nicolas Pepe's volley, with time still left for Dani Ceballos to hit the post.
Arsenal was quick out of the blocks and Aubameyang took full advantage of Burnley's meek resistance inside the box before his low effort beat Nick Pope at his near post despite the goalkeeper getting a hand to it.
Burnley, seeking a first league double over Arsenal since 1962-1963, should have fallen two behind midway through the half but Saka, on his 50th Premier League appearance, prodded wide after the ball fell kindly for him six yards out.
Instead, Sean Dyche's side was level at the break as Arsenal's attempts to play out from the back went calamitously wrong when Xhaka tried to pick out David Luiz and instead hit the ball straight into Wood's midriff.
Ben Mee and James Tarkowski each made excellent blocks to thwart Saka in the early stages of the second half as Arsenal continued to enjoy the majority of the chances.
Seeking inspiration from his bench, Arteta brought on Alexandre Lacazette inside the final half an hour, but Burnley then went close to a winner when Pieters, who had already survived one penalty shout after an apparent handball, had a dipping volley tipped over by Bernd Leno, who then denied Wood one-on-one.
There was late drama when Pepe's strike was deflected over by the industrious Pieters, with Marriner pointing to the spot and sending off the Dutchman before a VAR review showed the defender had somehow kept the ball out with his shoulder, while Ceballos cracked a shot against the upright as the spoils were shared.