Just a single change from last Sunday's loss to Tottenham Hotspur showed for the Gunners, as Mohamed Elneny filled in for the injured Thomas Partey.
Arsenal made a dominant start to the match with a volley from Alexandre Lacazette in the area following a cutback from Willian blocked by the opposing defence.
The Gunners weren't done piling on the pressure as the midway stage approached with a floating ball from Bukayo Saka nodded over the top of Nick Pope's goal by Rob Holding.
Pope was at work again before the closing quarter of the first half after diving across the goal-line to push Lacazette's low shot from point-blank range to safety.
The Clarets battled to get going in the second half, as a cross into the area from Kieran Tierney picked out Pierre-Emerick Aubameyang who stung the gloves of Pope.
Willian set the Gunners on course again inside 52 minutes after a low cross into the centre of the area brought Saka to a first-time strike which Pope beat away.
Arsenal were reduced to ten men following the 58th minute as a Video Assistant Referee (VAR) check gave Granit Xhaka his marching orders for grabbing Dwight McNeil by the throat.
The woes deepened for Mikel Arteta's side towards the last 15 minutes when Aubameyang headed a corner from the right-side into his own net amidst pressure from Josh Brownhill.
This forced Arteta to change his approach, as Eddie Nketiah replaced Willian moments later whilst Ainsley Maitland-Niles came on for Hector Bellerin.
It almost paid dividends with the Gunners closing in on the equaliser, but the day belonged to Sean Dysche's men who claimed all the points.