The Clarets are heading towards Christmas in the bottom three of the Premier League but showed the fighting spirit they will need to get out of trouble by pushing Arsenal all the way at the Emirates Stadium.
Burnley remain without an away success since the end of September and were unable to break the stranglehold Arsenal have inflicted on them in winning 10 of the past 11 fixtures between the two clubs thanks to two goals from Pierre-Emerick Aubameyang and an injury-time strike from Alex Iwobi.
But even taking into account last-minute winners in three of the last four meetings, few of those victories have had to be harder earned as Sean Dyche’s men bossed a second half book-ended by goals from Aubameyang and substitute Iwobi.
Ashley Barnes reduced the arrears with half an hour to go and the Clarets sniffed the possibility of a point as Arsenal were hanging on to try and close out the win that would keep them in touch with the top four.
But a second goal wouldn’t come and Burnley now return to Turf Moor for back-to-back home games against Everton and West Ham knowing they now need to put points to performances to give their survival bid added momentum.
With Aaron Lennon and Robbie Brady both on the injured list – and Johann Berg Gudmudsson not quite ready to return – the Clarets were shorn of all their senior widemen and named teenage defender Ali Koiki on the bench for the first time.
The changes meant a return for Chris Wood and Jeff Hendrick in a narrower midfield three and Wood as a forward partner for Barnes.
The result was an increase in attacking options and more of a threat going forward than the Clarets had provided at Tottenham a week earlier.
But Arsenal were also able to carry more of a cutting edge than their North London rivals had done and in a dramatic passage of play just two minutes in, both sides had chances to score.
It took the combined efforts of Joe Hart and James Tarkowski to keep Arsenal out with Hart saving well from Ainsley Maitland-Niles and Tarkowski bravely getting ahead of Aubameyang to block the follow-up.
And the Clarets then immediately broke away with Barnes releasing Ashley Westwood for an effort which would have brought the midfielder his first Burnley goal but for the toe-end of goalkeeper Bernd Leno.
The Clarets certainly had the ability to rattle an Arsenal side which had lost only twice in the Premier League at home in 2018.
But crucially the Gunners drew first blood after a quarter of an hour with the only goal of an occasionally fractious and feisty first half.
Club captain Mesut Ozil couldn’t get a game in Arsenal’s mid-week Caraboa Cup defeat to Tottenham but returned as captain here and showed a fleeting flash of class with a defence-breaking pass.
Left-back Sead Kolasinac was the beneficiary and when he knocked the ball back across goal, Aubameyang steered the ball into the corner of the net to claim his 12th Premier League goal of the campaign as Arsenal led at the break for the first time this season.
The Clarets were far from out of it, although three minutes into the second half their task became twice as difficult in the blink of an eye as Arsenal pounced to double their lead.
From pressing for an equaliser at one end, Burnley were suddenly undone on the break as Kolasinac and Alexandre Lacazette combined to release Aubameyang to rifle home his second of the afternoon.
That could have finished the Clarets, but they responded superbly.
Wood, despite looking well off-side, passed up a chance when he was slow to pull the trigger and Sokratis got back to clear before Kevin Long was pushed in the back by Kolasinac but Burnley’s wait for a Premier League game extended beyond a 60th game.
But with 63 minutes gone the Clarets were firmly back in the hunt as Barnes struck to raise hopes of a successful fightback.
Barnes had been a handful for the Arsenal defence all afternoon and got his reward when Long’s block following a melee in the penalty area fell for the striker to drive home his first Premier League goal since a double to help beat Bournemouth in September.
Jack Cork then had a sight of goal from Wood’s lay-off but sliced his effort wide as the Clarets gave everything to try and force an equaliser.
But the Gunners have made a habit of hurting Burnley with late goals and in stoppage time they grabbed a third to finally bank the points.
Again, the Clarets had to commit men forward and after breaking from inside his own half, Iwobi was then in the right place to collect a mis-hit shot from Ozil and slot home the goal which gave the scoreline an unflattering look for a Burnley side which could have given little more.
Arsenal: Leno, Maitland-Niles, Sokratis, Monreal (Lichtsteiner, 37), Kolasinac, Guendouzi, Elneny (Torreira 59), Xhaka, Ozil, Lacazette (Iwobi 78), Aubameyang. Substitutes: Cech, Ramsey, Nketiah, Saka.
Booked: Sokratis, Guendouzi.
Burnley: Hart, Bardsley (Lowton 83), Long, Tarkowski, Mee, Taylor, Westwood, Cork, Hendrick, Barnes Vokes 77), Wood (Vydras 77). Substitutes: Heaton, Lowton, Gibson, McNeil, Koiki.
Booked: Barnes, Wood, Mee, Cork
Referee: Kevin Friend