Ahmad Nourollahi gave the Reds a lead in the 10th minute.
Persepolis reduced to 10 men after Jerry Bengtson received his second yellow card in the 87th minute.
Four minutes later, Saipa striker Mehdi Daghagheleh found the back of the net.
Elsewhere, Tractor Sazi of Tabriz beat Sepahan of Isfahan 2-1 in Tabriz.
Rasoul Navidkia scored for Sepahan in the 13th minute.
Aloys Nong equalized the match in the 29th minute.
Sepahan midfielder Fozil Musaev was sent off in the 82nd minute and Mehdi Sharifi scored the winner for Tractor Sazi in the dying moments of the match.
Also, Zob Ahan of Isfahan was held to a 1-1 draw against Foolad in Iran's central city of Isfahan.
Mohammad Ahl Shakheh scored for the visiting team eight minutes into the match and Mehdi Rajabzadeh equalized the match in the 78th minute from the penalty spot.
Esteghlal Khuzestan and Esteghlal of Tehran are first and second in table with one game in hands and Persepolis remains third.