The Gunners went back to their preferred eleven after their FA Cup fourth clash against AFC Bournemouth, with Pierre Emerick Aubameyang, Mesut Ozil and Bernd Leno returning.
A first minute chance found Alexandre Lacazette who headed Aubameyang's looping delivery from good work by Ozil wide of Nick Pope's goal.
Burnley still managed to find their way despite the early scare; however Chris Wood failed to get past Bukayo Saka who cleared to safety.
A long ball from David Luiz on 14 minutes set up a clear opening for Aubameyang, who after staying onside fired the resultant effort wide of the near post.
The match opened up as the Clarets went through four minutes later, but Leno pulled across to smother Jay Rodriguez's attempt.
Pope came to his side's aid nine minutes before halftime after pulling out an outstretched hand to block Aubameyang's path to an open goal following a delivery from Granit Xhaka.
An injury to Saka straight after halftime ended his time on the field and was removed for Lucas Torreira.
Burnley fluffed a decent chance to go ahead on 56 minutes after James Tarkowski headed a free-kick into the area wide of the post.
The Gunners, who survived a mini onslaught from the hosts, regained confidence and Luiz went close to the opener on 71 minutes but found his attempt blocked.
Aubameyang had a chance to open the deadlock six minutes gone, but he headed Alexandre Lacazette's cross wide of the left-hand post.
Both sides pushed for the winner later on, but in the end a share of the spoils was what either side had to settle for overall.