Mehdi Torabi opened the scoring for the hosts in the 31st minute from the penalty spot and Isa Alekasir doubled the lead before the referee blew in the whistle just before halftime.
Reza Shekari pulled a goal back with a header in the 52nd minute.
The Sirjani team had several opportunities to equalize the game but they finally were unable to do so.
Persepolis are leading the Iran Professional League (IPL) above Sepahan-e Esfahan and Esteghla in the final weeks of the Iranian premier league.
Earlier in the day, Nassaji Mazandaran defeated Paykan 3-0.
Esteghlal and Havadar have already booked their place in the semifinals.
Hazfi Cup is the Iranian football knockout cup competition, run by the Iranian Football Federation. Esteghlal are the most successful club with seven titles.
Nassaji Mazandaran are defending champions of Hazfi cup.
KI
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