The pattern of the game was illustrated in the opening moments when Gunners 'keeper Manuel Almunia was forced to tip the ball against his own crossbar. However Burnley were unable to build on their early possessional advantage and fell behind when a mistake by Andre Bikey was seized upon by Cesc Fabregas who easily found the corner of Brian Jensen's net.
Indeed the visitors could have increased their lead shortly afterwards but Samir Nasri could only find the side netting with his effort.
The home team had another escape when Nasri found Andrey Arshavin whose shot beat Jensen but cannoned back off the post.
The game changed when Bikey was up-ended by central defender Thomas Vermaelen and Burnley captain Graham Alexander scored from the penalty spot, sending Alminia the wrong way.
Arsene Wenger's side suffered a blow when Fabregas had to leave with an injury to be replaced by Aaron Ramsey.
Whilst Arsenal enjoyed plenty of possession in the second period, Burnley were always dangerous on the counter attack and from such a move Chris Eagles brushed aside two challenges before seeing his shot strike a post.
Burley centre forward Steven Fletcher then shot over the bar and the same player thought he had scored the winner, turning in a cross from Eagles only for the assistant referee to disallow the goal for offside.
The home team's heroics ensured a well deserved point which re-enforces Burnley's home record that shows that Manchester United, Aston Villa, and now Arsenal all having failed to win on this ground.
This will be a frustrating result for Arsene Wenger's side who got themselves back into the Championship race with victory over Liverpool but in truth the Gunners did not deserve the three points as they failed to break down a stubborn Burnley rear guard in which defenders Clarke Carlisle and Stephen Jordan were outstanding.
Prior to the game Clarets boss Owen Coyle promised to go toe to toe with his illustrious opponents and the likeable young boss was true to his word as his side thoroughly deserved their point in their quest to maintain Premier League survival.