Martin Odegaard's first-half free-kick gave Arsenal their first away win of the season at Burnley.
The Norwegian curled home after Ashley Westwood had clipped Bukayo Saka on the edge of the area.
It was Odegaard's first goal since joining the Gunners on a permanent basis from Real Madrid in a £30m deal last month.
Burnley were denied a chance to equalise from the penalty spot when referee Anthony Taylor overturned his initial decision after reviewing Aaron Ramsdale's challenge on substitute Matej Vydra on the pitchside screen.
It was the high point of a spirited second-half performance by the hosts, whose manager Sean Dyche was this week given a new four-year contract and handed a debut to Ivory Coast wide-man Maxwel Cornet.
A second successive win eases Arsenal into mid-table following their poor start to the campaign, but Burnley remain second from bottom with a single point to show from their opening five games.
Arsenal making progress
As they had not lost at Turf Moor since 1973, Arsenal travelled north with some degree of confidence.
They were helped in extending their positive record by a strangely subdued home side, who were not a real threat until Cornet's introduction after 57 minutes.
Arsenal's midfield axis of Odegaard and Emile Smith Rowe either side of a deep-lying Thomas Partey was particularly effective, even if the goal threat of Nicolas Pepe and skipper Pierre-Emerick Aubameyang was negligible.
Still only 22, Odegaard still has plenty of time to prove why Real Madrid bought him as a 16-year-old in January 2015.
Although he only made 11 appearances for the Spanish giants, the Norwegian evidently has plenty of confidence.
He was happy to take responsibility from the set-piece after Westwood had fouled Saka and provided the perfect finish, over the ball and beyond the dive of Burnley goalkeeper Nick Pope.
Manager Mikel Arteta might have wanted more goal threat from his team, who dominated possession but surprisingly had fewer shots and corners than their hosts.
However, as the familiar "One-nil to the Arsenal" chant rang out at the end, Arteta could at least reflect on his side stabilising their terrible start to the season.
New contract, same old problem for Dyche
With his long-term future secure, Dyche has the green light to plot what he hopes will be the now-usual solid season at Turf Moor.
Yet with each passing year the task gets harder as clubs like Leeds and Aston Villa, with vastly superior resources, return to the top flight.
Once more, it appears Burnley lack firepower. Strike duo Ashley Barnes and Chris Wood have scored just one goal between them in six matches in all competitions and Burnley never really looked like improving on an awful record of 16 goals in their last 22 home league games.
Barnes should have done better when he headed Westwood's cross wide despite being unmarked, and although he beat the ground in frustration when another chance went begging, his chest control and volley while under pressure from two defenders was a hopeful at best.
Cornet's introduction gave the home fans a lift and the former Lyon man did bring a decent save out of Ramsdale.
But aside from the penalty shout, when Taylor mistakenly thought Ramsdale had taken Vydra down without touching the ball, Burnley never really looked like finding an equaliser.
The final whistle brought a prolonged period of baiting between the two sets of supporters, who gathered within yards of each other and hurled abuse, followed by a number of missiles.
A stadium announcement to clear the area initially went unheeded, although the crowds dispersed after around 10 minutes.