Mohammad Reza Soleymani scored the opener just 14 minutes into the match and Persepolis midfielder Ahmad Nourollahi made it 2-0 after he scored an own goal.
Persepolis goalkeeper Alireza Beiranvand played a key role in conceding both goals.
Newly-promoted Shahin Bushehr also beat First Division team Niroo Zamini 2-1 to reach the final match.
Persepolis, who is preparing to win the Iran Professional League for the fourth successive time, will meet Niroo Zamini on Friday while Saipa face Shahin Bushehr.