The meeting, which took place at the Emirates stadium in London, ended with a 1-0 victory for the guests.
The only goal of the match was scored by Arsenal striker Pierre-Emerick Aubameyang, who sent the ball into the net of his own goal.
From the 58th minute, the hosts played in the minority after the removal of Granit Jaki.
Arsenal are on the 15th line of the standings with 13 points.
Burnley scored ten points and moved up to 17th position.
Previously, Liverpool drew with Fulham in the 12th round of the Premier League.