Arsene Wenger's much-changed team, with an average age of under 20, were sunk by two-goal hero Kevin McDonald, who struck once in each half.
The Gunners, with former Northampton Town youngster Mark Randall in the side, had a number of chances to score themselves - including up to six one-on-ones - but Nicklas Bendtner, in particular, wasted several good positions and home goalkeeper Brian Jensen was equal to everything Arsenal threw at him.
Randall, who spent three years with the Cobblers before a successful trial saw him sold to the north London giants, was one of several youngsters named in the starting line-up by manager Wenger along with Welsh teenager Aaron Ramsey and 16-year-old Jack Wilshere.
But the Gunners were given a shock as Burnley took an early lead through McDonald.
Chris Eagles sent over a low cross from the right in the seventh minute and when Lukasz Fabianski failed to hold the ball on the edge of the six-yard box McDonald fired home.
Arsenal were stung and Bendtner sprung the offside trap in the ninth minute after a good through-ball from Carlos Vela but Jensen was equal to his effort.
Bendtner then produced a moment of great skill to play Randall into space, but the teenager shot early and Jensen was able to parry the ball away, while the keeper then made a superb save from Vela as half-time approached.
Randall was booked early in the second half for a foul on Burnley goalscorer McDonald, and the Gunners went further behind after 55 minutes when McDonald outmuscled Randall and shot home with the outside of his right foot.
McDonald soon left the pitch after receiving a knock while Randall was replaced by Amaury Bischoff.
Arsenal continued to create chances but Bendtner fired straight at Jensen when he should have scored and Wenger's side were unable to pull this one out of the fire.
Wenger: Randall is an exceptional talent - click here
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