Armin Sohrabian opened the scoring for the Blues in Tehran’s Azadi Stadium in the 61st minute and Peyman Babaei, who came off the bench in the second half, scored the second goal for Esteghlal in the 72nd minute.
Paykan forward Amir Shahim pulled a goal back in the injury time.
Esteghlal sits top with 32 points, one point above Sepahan.
Earlier in the day, Tractor defeated Sanat Naft 3-0 in Tabriz, thanks to goals from Aref Aghasi (25th), Mehdi Hashemnejhad (32nd) and Mohammad Ghanbari (77th).
On Sunday, Aluminum will host Malavan in Arak and Havadar face struggling Esteghlal Khuzestan in Tehran.
Sepahan will host Shams Azar in Isfahan, while Persepolis travel to Rafsanjan to meet Mes on Monday.
On Wednesday, Zob Ahan will play Gol Gohar in Isfahan and Foolad meet Nassaji in Ahvaz.