Ali Alipour got the designated visitor on its way with a cool finish after five minutes, only for Saleh al-Amri to net an equalizer for Al Ahli seven minutes into the second half, Fox Sports reported.
However, Persepolis reclaimed the lead through a Godwin Mensha penalty in the 83rd minute, before Mahdi Taremi converted a second spot-kick in injury-time to seal the progress with a 5-3 aggregate triumph.
Having conceded two away goals in a 2-2 first-leg draw three weeks earlier, Persepolis entered the tie at the Mohammed Bin Zayed Stadium knowing it would be in a precarious position as long as the Iranians failed to score.
Alipour settled some of the nerves just five minutes in as he chased down a hopeful ball and shrugged off the challenge of Mohammed al-Fatil, before finishing past Mohammed al-Owais.
But just six minutes later, the Persian Gulf Pro League champion was dealt a huge blow when Kamal Kamyabinia was sent off for a studs-up challenge on Waleed Bakshween.
Despite being a man down, Persepolis continued to show more endeavor and was arguably the better of the two sides throughout the first half.
Nonetheless, Al Ahli eventually found the equalizer in the 52nd minute; al-Amri gliding past a challenge and bending a lovely shot into the far corner.
It now looked as though the Saudi giant would go on to claim the ascendancy yet its opponent refused to budge.
Persepolis piled the pressure in pursuit of a winner and as in the first leg encounter three substitutions made by Branko Ivankovic turned things around for Iran’s champion.
Whenever it could, Persepolis still looked to attack and was rewarded for its efforts in the 81st minute when a goal-bound shot from Shayan Mosleh was handled on the line by Motaz Hawsawi.
The referee had no hesitation in pointing to the spot and issuing Hawsawi his marching orders.
When the dust settled, it was Mensha who took on the responsibility for the Iranians and coolly sent al-Owais the wrong way.
It was now just a matter of seeing out the remainder of the contest but Persepolis had other ideas.
Right at the death, the Iranian Reds won another penalty after Bashar Ressan was brought down in the eighteen-yard box and, this time, it was Taremi who converted from the spot, confirming his side’s semifinal meeting with another Saudi side in Al Hilal.