The Reds shared the points with Shahrdari at Tehran's Azadi Stadium on Friday to remain fourth in the table.
Persepolis fought hard to earn the critical three points from the home match and created many good scoring opportunities, but fell short in the end.
Persepolis has collected 44 points while Shahrdari has 25 points and is in 15th spot of the IPL table.
Earlier in the day, titleholder Sepahan defeated Naft Tehran 2-0 to close the gap with league pacesetter Zob Ahan.
Two minutes into the hour mark Kianoush Rahmati scored the opener, and Ehsan Hajsafi doubled the lead for Amir Qalenoei's side in the 81st minute of the game.
Sepahan stands second with 49 points, one behind its city rival Zob Ahan, which is leading the 18-team league table with 50 points.
In another game on Friday, Naft Abadan blanked star-studded Steel Azin 2-0, giving new coach Gholam-Hossein Peyrovani a win in his debut match.
On Thursday, the game between Zob Ahan and Rah Ahan ended in a 2-2 tie. Rah Ahan sits in 12th place with 29 points.
Also on Thursday, the popular Tehran club Esteqlal and Saipa played to a goalless draw at Tehran's Azadi Stadium. The Blues are currently in third place and Saipa is in 11th in the standings.