Ali Alipour scored two goals for the visiting team in the 59th and 72nd minutes.
Naft Masjed Soleyman also defeated Shahin Bushehr 3-2 in Masjed Soleyman.
Esteghlal was scheduled to host Sepahan on Monday but the match was canceled to air pollution.
Tractor will also meet Mes Kerman.
Hazfi Cup is the Iranian football knockout cup competition, run by the Iranian Football Federation.
The competition was founded in 1975. Esteghlal is the most successful club with seven titles.