An early goal from Pierre-Emerick Aubameyang gave Arsenal the lead for 40 minutes before a defensive error allowed Chris Wood to equalise.
Aubameyang in fine form
Aubameyang's early goal knocked Burnley early on. The Gabonese striker cut inside, beating Tarkowski and fired one low past Nick Pope, who should have saved it.
The striker has now scored nine in 23 league games and has proved to be Mikel Arteta's star man this season.
Since joining the London based side he has scored 84 in 137 games. Arteta need's to make sure he keeps Aubameyang at the focal point of his attack if Arsenal are to challenge for Europe again next season.
Arsenal thought they had won the game in added time when Dani Cabellos rattled the post after a scramble of chances in the box.
It shows just how close Arsenal have come numerous times and shows their inconsistency when it comes to results. They had entered this game off the back of a 3-1 with Leicester City but failed to capitalise on that this weekend.
It could be a missed opportunity to push themselves closer to a guaranteed top 10 position in the league as their next game is the North London Derby.
Capitalising on mistakes
Burnley equalised five minutes before the half through Wood after a shocking defensive mistake by Granit Xhaka. Xhaka's failed clearance bounced off Wood's hip and into the net.
Wood was in that position due to the high press that Burnley had been putting onto Arsenal. Towards the end of the first half, the Gunners sat back and invited Dyche's men to get further forward which resulted in the goal.
The goal just before the break seemed to change the climate of the game. Burnley came out the break looking more solid at the back and looked to have more threat going forward.
Erik Pieters block
Arsenal though they had a chance to finish the game off just a few minutes from time after a penalty was given for handball. Erik Pieters blocked a shot off the line with what originally looked like his hand, forcing Andre Marriner to point to the spot.
However, VAR was bought into check the decision and both the penalty and the second yellow sending off was overturned after the replays showed the ball hitting Pieters' shoulder.
The decision is crucial for Burnley who took a solid point, that will help with their survival chances, away from a tough fixture.