Esteghlal went ahead through Khosro Heydari on 24 minutes despite being without key midfield duo Andranik Teymourian and Mojtaba Jabbari.
Top goalscorer Jabbari was sidelined with a knee complaint but on-loan Cardiff defender Jlloyd Samuel came into the starting XI and the home side were in total command.
Arash Borhani doubled Esteghlal's lead in the 67th minute and sealed their passage through to the second round of the playoffs where they will meet Saudi Arabian side Al Ettifaq.
Zob Ahan were seeking a third consecutive appearance in the competition after making the quarter-finals last year and finishing runners-up in 2010.
Esteghlal now face Al Ettifaq for a place in Group A alongside Qatar's Al Rayyan, Al Jazira of the United Arab Emirates and 2011 AFC Cup winners Nasaf from Uzbekistan.