Pierre-Emerick Aubameyang, who scored an own goal in the meeting at the Emirates, put Arsenal ahead when beating Nick Pope at his near post.
The Gunners had opportunities to extend their lead through Bukayo Saka, Aubameyang and Thomas Partey, but the Clarets weathered the storm.
And Sean Dyche's side were gifted an equaliser before the break when Granit Xhaka, attempting to play the ball across his own penalty area, saw his pass ricochet off Chris Wood and into the net.
Erik Pieters, who replaced Charlie Taylor in the 63rd minute, was in the thick of the action following his introduction.
The Dutchman tested Bernd Leno with a tremendous dipping volley from distance and then saw a red card overturned having diverted Nicolas Pepe's shot onto the crossbar.
Wood almost snatched the points for the hosts when denied by the legs of Leno from Matej Vydra's cross before Calum Chambers smashed an effort against the post at the other end.
9. Josh Brownhill 6.4
Reverted back to his central role in midfield, but struggled to take any control in the first half. Worked well alongside Westwood in the second half to obstruct passing lanes for the Gunners while trying to calm things down on the ball.
10. Matej Vydra 7.7
Put his heart and soul in to today's performance. Stepped up the energy in the second half and the rest of the side followed his lead. Fought tooth and nail for every ball, turned the play over and put the ball on a plate for Wood.
11. Chris Wood 7.1
Got the better of Luiz and Mari in aerial tussles and linked play well. Scored a fortuitous equaliser, but the finish will do him the world of good. Could have wrapped up the three points when denied by Leno in the second half.
12. Erik Pieters 7.2
Involved in absolutely everything after his introduction. In 25 minutes he almost scored a spectacular volley, survived a handball scare and had a red card (rightly) overturned after turning Pepe's strike onto the bar. Always in the thick of it.