The Clarets failed to upset the odds but didn't go down without a fight as they proved there is still life in their survival bid ahead of a big week back at Turf Moor.
Burnley were any price with the bookmakers to derail Arsenal's championship bid thanks to the worst away record in the Barclays Premier League.
And while Theo Walcott's 60th-minute goal and an injury-time effort from Andrey Arshavin kept Brian Laws' men in the bottom three, the Clarets pushed Arsene Wenger's men all the way.
Arsenal did miss a clutch of chances but Burnley did what they have failed to do so many times away from home this season - stay in the game.
With Brian Jensen defiant in goal and the Clarets scrapping for everything they cancelled out Cesc Fabregas's first-half goal with an excellent finish from David Nugent just after the break.
And Arsenal were hanging on before Arshavin's late strike as Burnley showed the character they now need to produce points against Stoke and Wolves in crucial back-to-back home games.
David Nugent strikes to level at 1-1
The Clarets were without top scorer Steven Fletcher with a hand injury but Laws was able to bring back Graham Alexander as captain and also gave starts to Nugent, Chris Eagles and Jack Cork as he tried to find a formula to stop the rot away from home.
The Emirates Stadium was always likely to be a tough place to break the spell and the Clarets inevitably had to soak up some early pressure.
Niklas Bendtner got in the behind the Burnley defence after just three minutes but Martin Paterson's excellent covering tackle saved the day with Jensen pushing the loose ball round the post.
Walcott, who had flopped in mid-week on England duty, looked a different player as he stretched Burnley down the right, while Fabregas orchestrated things from central midfield for the title hopefuls.
Fabregas combined with Emmanuel Eboue for a chance which Fabregas dragged wide and also with Samir Nasri who was thwarted by a combination of Tyrone Mears and Jensen.
And when Eboue crossed low Jensen was again called on to save from Bendtner.
And the Clarets celebrate
It was not all one-way traffic, though, as Burnley battled to get a foothold in the game.
Clarke Carlisle had headed an early chance at Manuel Alminia from a Danny Fox corner and the Spanish keeper also had hold long-range efforts from Fox and Paterson.
But just when the Clarets looked as though they might start to frustrate the Gunners they went behind with 11 minutes to go to half-time.
Burnley had plenty of men between Nasri and the goal but the Frenchman by-passed with a beautiful lofted pass over the wall of white shirts for Fabregas to run beyond Alexander and poke a shot between Jensen's legs.
Fabregas limped off shortly afterwards, as he had done at Turf Moor in December when Arsenal were leading 1-0 and seemingly in control.
And as in that game, Burnley hit back to level five minutes after the break.
Cesc Fabregas puts the Gunners ahead
Bendtner should have put the game beyond the Clarets but missed two excellent chances within minutes of the re-start and Nugent made him pay.
It had been a tough afternoon for Nugent in a lone role up front but the striker was razor-sharp when the chance came his way to snaffle his fifth goal of the season and stun the Gunners.
Leon Cort's forward header split the Arsenal defence and Nugent pounced to lift the ball past Almunia on the volley from 12 yards out.
The Clarets' fans erupted in their corner of the stadium but unfortunately for them their side was level for just ten minutes.
Arsenal went straight back on the offensive and after Bendtner has passed up another chance Walcott made it 2-1 on the hour.
The winger cut inside onto his left foot and with a low shot beat Jensen into the far corner to cap an outstanding performance.
Graham Alexander challenges Samir Nasri
The same adjective could not be attributed to Bendtner who missed from in front of goal from another Walcott cross before being dragged off and with just a one-goal deficit the Clarets sensed they could nick a point.
As Arsenal got edgy Burnley, with Chris Eagles finishing strongly and Steven Thompson on up front in tandem with Nugent, pressed forward and almost forced an equaliser five minutes from the end.
A Fox corner dropped for Thompson and the substitute almost crowned a lively cameo with a stunning goal as he cracked a volley just over the bar to the relief of an Arsenal side which needed an injury-time strike from Arshavin to settle their nerves.
Burnley: Jensen, Mears, Carlisle, Cort, Fox, Alexander (Bikey 66), Eagles, Cork, McDonald (Elliott 54), Paterson (Thompson 74), Nugent. Subs: Duff, Blake, Jordan, Weaver.
Arsenal: Almunia, Eboue, Vermaelen, Silvestre, Clichy, Denilson, Walcott, Fabregas (Diaby 39), Nasri, Rosicky (Arshavin 61), Bendtner (Eduardo 74). Subs: Sagna, Traore, Eastmond, Fabianski.
Referee: Chris Foy
Booked: McDonald 27, Paterson 48, Carlisle 69, Elliott 72
David Nugent gets away from Samir Nasri