The Clarets’ Arsenal jinx struck again as the Gunners grabbed an injury-time winner for the third time in a row.
Burnley were in touching distance of another point against top-six opposition as they looked to extend their best start to a season in 43 years thanks to a fourth successive clean sheet.
But fortune deserted them again when referee Lee Mason awarded a penalty for a push by James Tarkowski on Aaron Ramsey and Alexis Sanchez scored from the spot to hand the Clarets a first home defeat since August.
It was tough to take for Sean Dyche’s side, who were also undone home and away by controversial stoppage-time winners against the Gunners last season, Laurent Koscielny bundling the ball home with his arm at Turf Moor and Sanchez also scoring from the spot at the Emirates Stadium after an off-side decision was missed in the build-up.
This was another tough call as Tarkowski was punished at the end of afternoon when he and his defensive side-kick Ben Mee again put in towering performances in front of watching England boss Gareth Southgate.
Mason's decision - after Ramsey went to ground in dramatic style - meant it was Arsenal, rather than Dyche's men, who claimed the top-four spot on offer, despite having arrived at Turf Moor just 50 minutes before kick-off.
Arsene Wenger's men were then almost caught cold by a blistering Burnley start as the Clarets looked to continue a run which had already seen them take points from three sides above them in the table.
The Clarets – unchanged from the starting line-up that had made it three top-flight wins in a row for the first time since 1975 with victory over Swansea last weekend – came flying out the blocks as they made sure the Gunners would have no time to find their feet.
Johann Berg Gudmundsson and Robbie Brady set the tone as they tore into the visitors from wide positions.
And it was that pair that came close to combining to give the Clarets a 15th-minute lead.
Brady won possession with a terrific tackle before finding Jeff Hendrick. Hendrick helped the ball on to Gudmundsson, who turned past Nacho Monreal before letting fly with an angled drive which Petr Cech pushed onto a post.
The officials didn’t spot the save, Steven Defour earning a booking for protesting at the award of a throw-in to the Gunners, who were glad of the respite.
Defour and Jack Cork, doubtless also on Southgate's radar, were again instrumental in keeping Burnley moving forward and it took a brave block from Shkodran Mustafi to stop a fierce Defour strike as the Clarets tried to make one of their five first-half corners count.
Brady’s delivery provided a constant threat and the Ireland international also tested Cech with a free-kick six minutes before the break which the veteran keeper was glad to parry away.
Arsenal, missing the unwell Mesut Ozil, struggled to make an impact against a Burnley back line which hadn’t conceded a goal during the current winning streak.
But there were a couple of moments of concern for the Clarets before the break as Nacho Monreal fizzed a long-range effort just wide and Ramsey failed to hit the target after the elusive Alexandre Lacazette had given Tarkowski the slip and delivered a perfect low cross.
And having warmed to their task, Arsenal started the second half with their best period of the game.
The Gunners were camped in Burnley territory for spells, with Sanchez finding pockets of space and Sead Kolasinac launching a number of dangerous runs from left wing-back.
But the Clarets refused to buckle with Tarkowski and Mee again proving impassable and on the break there was still the prospect of a goal from Dyche’s men.
The outstanding Gudmundsson warmed Cech’s hands again after cutting inside to unleash a drive from 25 yards before the Irish trio of Hendrick, Stephen Ward and Brady linked superbly for Brady – enjoying one of his best games in a Burnley shirt – to fire in a shot which was blocked by Koscielny.
The Clarets, putting on an additional striker in Chris Wood for the closing stages, didn’t give up hope of pressing for a winner.
But Arsenal also went in hunt of maximum points and only a second away win of the campaign and nicked it in stoppage time yet again.
Kolasinac’s headed ball into the penalty area was aimed for Ramsey and when he went down in exaggerated style under pressure from Tarkowski, Mason pointed to the spot.
Sanchez’s spot-kick just squeezed under the outstretched arm of Nick Pope, with a first goal conceded since losing to league leaders Manchester City last month cruelly denying the Clarets the point they deserved as lightning struck for a third time.
Burnley: Pope, Lowton, Tarkowski, Mee, Ward, Gudjonsson, Cork, Defour (Wood 79), Brady, Hendrick, Barnes. Substitutes: Lindegaard, Vokes, Westwood, Bardsley, Long, Arfield.
Booked: Defour, Brady.
Arsenal: Cech, Koscielny, Mustafi, Monreal, Bellerin, Ramsey, Xhaka, Kolasinac, Iwobi (Wilshere 67), Alexis, Lacazette (Welbeck 79). Substitutes: Ospina, Mertesacker, Giroud, Maitland-Niles, Coquelin.
Referee: Lee Mason
Attendance: 21,722 (2,451)