Mohsen Mosalman opened the scoring for the home side on the dying seconds of first half with a left foot effort before Alireza Ramazani doubled the lead for Malavan on the 78th minute from the penalty spot on Thursday.
Tehran Reds were gifted a windfall opportunity to draw level on the 68th minute after Malavan's captain Babak Pourqolami handled the ball inside his own penalty area for the referee, Alireza Faqani, to point to the spot.
However, Mehdi Mahdavikia, who had switched to Persepolis from Damash Gilan on a 6-month deal earlier this week, squandered the chance after seeing his penalty saved by Malavan goalkeeper Ali Hassani Sefat.
The defeat leaves Perseplolis on 9th place in the 18-team table with 22 points, while Malavan hauled itself up to the 16th spot with 18 points.
Naft Tehran moved within three points of Iran Pro League leaders Esteghlal with a 1-0 home win over Fajr Sepasi.
Mohammad Mehrazma scored the only goal of the game after 10 minutes to seal the points for the second-placed side.
Elsewhere, Rah Ahan triumphed 2-0 at Zob Ahan thanks to goals from Omid Alishah and Alireza Abbasfard, while Ghasem Dehnavi's effort shortly before half-time saw Mes defeat Shahrdari Tabriz 1-0.
In the day's other games Mes of Kerman downed the hosts Shahrdari of Tabriz by a single goal, Zob Ahan of Esfehan suffered a home defeat to Rah Ahan by two goals to nil, and Naft of Tehran overcame visitors Fajr-e-Sepasi by a solitary goal.