The defending champions stood in Iran Premier League's (IPL) first place with eight points after four weeks on Friday night.
The match was stopped for about half an hour after 20 minutes for a sudden power failure.
Esteqlal could have scored a goal through Khosro Heidari when his powerful shot hit the bar and Malavan was unlucky when Mohammad Nezhati's shot hit an Esteqlal defender after passing goalkeeper Vahid Taleblu in stoppage time.
Esteqlal and Malavan have so far played 41 matches against each other. Esteqlal has won 17 and Malavan 6 matches. They drew 18 other matches.
The Blues, under Samad Marfavi, earlier defeated Sepahan 1-0 in their opener drew 0-0 with Mogavemat and beat Foulad 1-0 at Tehran's Azadi Stadium.