The Reds beat Mes as 20,000 spectators watched at Tehran's Azadi Stadium on Friday afternoon.
Persepolis defender Sepehr Heidari broke the deadlock four minutes after the break and striker Mohsen Khalili doubled the lead in the 71st.
"The victory against Mes was a gift to our fans," Persepolis Croatian manager Zlatko Kranjcar told reporters at a press conference after the game.
"Our players showed that they can defeat their rivals with unity," he added.
Mes Kerman coach Mehdi Mohammadi also said that Persepolis deserved to win the match.
"Persepolis fully deserved their win over Mes," Mohammadi said at the press conference.
Sepahan currently tops the standings with 34 points after 18 matches, followed by Zob Ahan on 33. Moqavemat sits third with 30 while Persepolis is fourth on 29.
The Tehran-based Esteqlal is scheduled to face Sepahan at the Foolad Shahr Stadium in Isfahan on Saturday.
Other Friday match results:
Saipa 2-1 Zob Ahan
Foulad 4-0 Rah Ahan
Moqavemat 1-0 Peykan
Abumoslem 2-0 Esteqlal Ahvaz
Malavan 0-0 Shahin
Teraktorsazi 3-0 Saba