The Tuesday victory was the Reds' first under Nelo Vingada, who was appointed as Persepolis' new manager 10 days ago.
A slow first half saw the two sides failing to make goal attempts and create chances. Three minutes into the second half, however, Karim Baqeri's powerful shot from outside the 18-yard-box was deflected by Abumoslem's defender to find its way to the back of the net.
Abumoslem's goalkeeper Shahab Gordan was sent off ten minutes later after hitting a ball-boy in the face with the ball. After the match Gordan was suspended indefinitely by Iran's Football Federation.
The victory sent Persepolis to the second place with 47 points out of 27 games played, while Esteqlal leads the table with 53 points out of 26 games played. The Blues will face Moqavemat on Wednesday.
Third-placed Zob Ahan, which also has 47 points, would reclaim the second spot should it avoid defeat against Rah Ahan on Wednesday.
In another Tuesday match, Sepahan beat Barq 1-0 to stand in the fourth place with 44 points.