Burnley looked to have deservedly earned a point until, at a short-corner routine, substitute Alex Oxlade-Chamberlain sent Theo Walcott’s flick towards goal at the far post. The close-range effort looked to find the net off the hand of teammate Koscielny, who was stationed virtually on the goal-line.
Along with the suggestion of handball, both Arsenal players appeared offside, but referee Craig Pawson was unmoved by the ensuing Burnley protests at Turf Moor.
A fifth consecutive league win lifted Wenger’s side up to third, two points behind leaders Manchester City and a point drift of north London rivals Tottenham Hotspur in what looks increasingly like being an open title race this season.
It was a contest neither side deserved to lose, although Arsenal almost found the net before the disputed winner, when Walcott’s curling 20-yard effort drifted inches wide of Tom Heaton’s left-hand post.
Defeat was extremely harsh on Burnley, who remain 14th on the back of another hard-working performance full of character, as they continue to impress on their return to the top flight following promotion in May.
They nearly broke the deadlock when, with 15 minutes left, recalled keeper Petr Cech touched defender Michael Keane header against the Arsenal bar as the visitors posted a fourth consecutive clean sheet, a run spanning more than six hours.
Cech had also been forced to save well from a Johann Berg Gudmundsson header early in the second-half as the Clarets aimed for a repeat of their victory over Liverpool earlier in the season.
Ian Wright scored twice as Wenger’s celebrated reign, which boasts three Premier League titles and six FA Cups, started with a 2-0 win at nearby northwest side Blackburn Rovers back in 1996.
This victory was rather less clearcut, although Arsenal rarely looked in danger at the outset of their latest visit to Lancashire.
Sam Vokes, the Wales international, had proved a threat throughout with his physical presence and restless work-rate.
However, Burnley’s lone forward should have done much better when he headed wide from near the penalty spot after meeting Matt Lowton’s cross from the right unmarked after being played onside by Hector Bellerin.
It was an opening against the general run of play, as Arsenal enjoyed two-thirds of possession and greater territory without making their dominance pay.
They were rationed to half-chances by a Burnley back-four in which Chelsea target Keane again excelled.
Alexis Sanchez, aiming to find the net for the fourth time in four appearances against the Clarets, saw his angled drive deflected inches wide by defender Ben Mee in an early foray, before Walcott fired across the face of goal at the culmination of a neat three-man move.
It was early in the second half when Tom Heaton was called on to make his first notable save, the Burnley goalkeeper diving smartly to his left to hold a close-range effort from Sanchez, after some intricate build up play from Walcott and the otherwise largely anonymous Mesut Ozil.
Sanchez went even closer inside the final 20 minutes, grazing the post with a close-range volley, before Arsenal’s late pressure eventually told in a heart-breaking finale for Sean Dyche’s side.