The hosts took the lead when Iman Razzaqirad scored the only goal of the game after 64 minutes on Sunday night.
"We defeated Steel Azin by controlling its playmaker Ali Karimi," said Peykan's coach Hamid Derakhshan after the match.
'Our defensive players showed a rational performance to prevent Steel Azin's top players from scoring," he added.
Steel Azin manager Hamid Estili, however, blamed his side's first failure this season on a lack of confidence.
"One of the main reasons for our defeat was our players' lack of confidence," Estili said.
"Steel Azin has just advanced to the country's Premier League but it will undoubtedly perform better in the coming weeks," he added.
"Peykan took full advantage of our defensive mistakes to gain all three points in the game," he further explained
According to Stili, rivals have analyzed Peykan's key players and keep them from playing well by controlling them.
Next week, Steel Azin will face Tehran's popular Esteqlal team, which tied 1-1 with Teraktorsazi in front of 80,000 spectators at the Yadegar-e-Emam Stadium in Tabriz last night.
Esteqlal's skipper, Farhad Majidi, headed the opener for the Blues in the 25th minute while Moahammad Ebrahimi scored the equalizer ten minutes from time.
Peykan currently stands atop the IPL with 13 points followed by Moqavemat and Esteqlal which have 12 points apiece.
The results of other Sunday matches are as follows:
Mes Kerman 5-2 Zob Ahan
Sepahan 3-1 Pas
Saipa 1-1 Moqavemat
Malavan 1-0 Foulad
Abu Moslem 1-1 Rah Ahan
Saba 1-0 Estqlal Ahvaz