Al Ahli's defence failed to deal with a long throw-in from Mehdi Shiri and defender Shojae Khalilzadeh was in the right spot and went for the spectacular, volleying home from inside the box past a helpless Mohammed Al Owais.
Two minutes later, Ahmad Noorollahi tried his luck for Persepolis from distance, but his shot missed by inches.
Al Ahli had to wait until the 34th minute to get their first chance. Djaniny received Abdulfattah Asiri's pass and rifled from 30 yards out, but his ball went high over the crossbar.
Persepolis came racing out of the blocks in the second half and within three minutes, they had doubled their lead through Ali Alipour.
With the result, Persepolis climb into third place with four points, while Al Ahli drop to the foot of the group ahead of the reverse fixture in Dubai on April 22.