With five weeks remaining, the Reds are on the verge of winning the IPL title for the third year in a row.
Saipa forward Moein Abbasian scored an early goal in the 4th minute but Bashar Rasan leveled the score, firing a superb shot home from the edge of the area in the 32nd minute.
Ali Alipour scored Persepolis second goal in the 50th minute and substitute Mehdi Torabi made it 3-1 just after the hour mark.
Reza Asadi pulled a goal back in the 68th minute.
Persepolis remain at the top of the table with 54 points, followed by Tractor Sazi with 49 points.
Esteghlal and Sepahan are third and fourth with 47 points, followed by Padideh with 46 points.