Two teams finished in a 1-1 draw after extra time and Qashqaei defeated Persepolis 6-5 in penalty shootout.
Elsewhere, Tractor Sazi defeated Foolad Yasuj 2-0.
Esteghlal of Tehran has been scheduled to meet Malavan Novin on Saturday in Bandar Anzali.
The 2016–17 Hazfi Cup is the 30th season of the Iranian football knockout competition. Zob Ahan Isfahan is the defending champion. The final will be played on 23 May 2017.