The loss is the third straight in the league for Mikel Arteta's team and the fourth straight home loss - their worst home result since December 1959.
The unimaginative attacking play did not give the strong defensive-minded bottom team Burnley any major problems before the break.
The sharpening came in the second, but then midfielder Granit Xhaka showed weak impulse control and received a red card for a stranglehold on an opponent.
Pierre-Emerick Aubameyang has had a lousy start to the season, but now the striker scored, the first home of the season at the Emirates.
Unfortunately, it was in their own goal - and the only match.
Arsenal are first in 15th place in the league after 13 points in twelve games, and the pressure on coach Arteta is increasing.