Barnes’ first-half equaliser to cancel out Alexandre Lacazette’s early effort gave the Burnley frontman his third goal of the season.
He also scored home and away against the Gunners last season and his latest contribution took his tally of Premier League goals this calendar year to a dozen.
Only Sadio Mane and Sergio Aguero have scored more – Mane’s haul helping him share last season’s Premier League golden boot with Liverpool team-mate Mo Salah and Pierre-Emerick Aubameyang.
And like Barnes, Aubameyang has also started the new campaign on fire and after scoring the Gunners’ winner at Newcastle United last weekend, the Gabon international repeated the trick with the goal that nipped Burnley’s fightback in the bud and gave Arsenal a 10th successive win in the fixture.
Unsurprisingly, the Clarets were unchanged from their opening-day win over Southampton, with Charlie Taylor’s the return among the substitutes the only alteration to the match-day squad.
And like Barnes, Aubameyang has also started the new campaign on fire and after scoring the Gunners’ winner at Newcastle United last weekend, the Gabon international repeated the trick with the goal that nipped Burnley’s fighback in the bud and gave Arsenal a 10th successive win in the fixture.
Arsenal also collected three points first up thanks to Aubameyang’s goal but opted to change their winning formula as new signings David Luiz and Dani Ceballos made their home debuts.
There was also a return to starting duty for Lacazette and it was the France international who made biggest impact with the opening goal 13 minutes in.
The Clarets needed to ride out an early spell of pressure but cracked from an Arsenal set-piece.
rom Lacazette and when Ceballos delivered the resulting corner, the Arsenal’s number-nine showed the necessary strength to hold off Erik Pieters on the turn and drill a shot through the legs of Pope at the near post.
The Clarets had been slow to make their presence felt following the early kick-off but responded well to going behind.
Immediately Burnley had a chance to equalise but from Pope’s long clearance Barnes dragged his shot just wide.
And Sean Dyche’s men then continued to unsettle the Gunners as they pressed high up the pitch and threatened from a number of set-pieces of their own.
The danger came from Arsenal on the break and Pope had to save with his feet to keep out a low strike from Matteo Guendouzi.
But two minutes before the break the Clarets deservedly equalised through that man Barnes, who has now scored 13 times against the top-flight’s ‘big six’..
This time it was Burnley who struck on the counter-attack as Chris Wood got free to lay the ball back to Dwight McNeil.
The teenage winger had been a growing influence and although his shot was half blocked, the ball fell to the predatory Barnes to keep his composure and hold off Luiz to roll a shot into the bottom corner and send the sides in level – a VAR decision upholding that of the assistant referee to disallow a Reiss Nelson strike for off-side against Nacho Monreal with the last kick of the half.
Arsenal’s reaction was to send on £72m record buy Nicolas Pepe at the re-start and, as in the first period, the Clarets had to weather some early probing.
When Pope stayed big to make a fine block from Aubameyang and then pulled off another smart save at full length to turn away a Ceballos effort it looked as though they might come through it.
But Aubameyang has been a constant thorn in the Clarets’ side and after scoring twice in both legs of the Gunners’ double last season he struck again with just over an hour gone, steering a shot into the bottom corner from 20 yards out after Ceballos had robbed Johann Berg Gudmundsson on the Icelander’s 100th Burnley appearance.
Gudmundsson looked to counter-punch with a cross at the other end which McNeil headed over the top from an inviting position to mirror an earlier effort from Ashley Westwood when the scores were still level.
But the Clarets were unable to get another clear sight of goal as they scrapped for a first point at this ground.
Pope kept them in the hunt with another smart block from substitute Lucas Torreira and the Clarets’ keeper almost played a part in a dramatic late equaliser when he came up for a corner.
Pope connected with a header, but James Tarkowski couldn’t feed sufficiently off the scraps to propel his own effort goalwards as a relieved home side scrambled the ball clear to hang on to all three points and maintain their monopoly.
Arsenal: Leno; Maitland-Niles, Sokratis, Luiz, Monreal; Guendouzi, Willock; Ceballos (Torreira 83); Aubameyang, Lacazette (Kolasinac 72), Nelson (Pepe HT). Substitutes: Martinez, Mkhitaryan, Chambers, Martinelli.
Booked: Aubameyang, Luiz.
Burnley: Pope; Lowton, Tarkowski, Mee, Pieters; Gudmundsson (Lennon 72), Cork, Westwood, McNeil; Barnes, Wood (Rodriguez 61). Substitutes: Hart, Taylor, Hendrick, Gibson, Bardsley.
Referee: Mike Dean