In the match, held at the Martyred General Qassem Soleimani Stadium, Mehdi Torabi found the back of the net in the 85th minute from the penalty spot.
In Bushehr, Zob Ahan moved up to 10th place after earning a 5-1 win over Shahin Busher.
Ehsan Pahlavan opened the scoring for the visiting team in the 26th minute. Serbian midfielder Ivan Markovic made a brace in the 41st and 58th.
Mohammad Nejadmahdi and Danial Esmaeilifar also were on target in the 50th and 59th minute, respectively.
Hassan Najafi scored a consolation goal for Shahin in the 69th minute.
With six week remaining, Persepolis leads the table with 56 points.