The Iranians secured the win at Azadi Stadium courtesy of a Mohsin Khalili strike a minute into the second half and ensure first place in the standings due to a better head-to-head with Al Shabab.
Piroozi will play Bunyodkor of Uzbekistan in the last 16 on May 27.
Al Shabab started strongly and created the first opportunity after just five minutes when Abdulaziz bin Saran picked up a pass from Abdullah Shuhail but his shot flew wide.
The visitors had another chance after 13 minutes when Abdoh Autef’s effort hit the Iranian defence and Saran pounced to send a powerful shot from close range that was pushed away for a corner by Misagh Memarzadeh.
Al Shabab went close again when Autef latched onto a long ball from the back to smash a powerful strike just wide of the left upright.
The tempo of the game slowed down after that as Piroozi struggled to impose themselves while Al Shabab were happy to keep their opponents at bay and avoid taking risks.
But Piroozi made an explosive start to the second-half and took just 40 seconds to open the scoring in bizarre fashion.
Pejman Nouri played a corner from the left that deflected off the Al Shabab defence and the ball fell to Khalili and though his first time effort was cleared by Abdullah Shuhail, the ball bounced back to the Piroozi attacker and hit his stomach before landing in the back of the net.
Khalili should have scored his second goal of the night five minutes after the hour mark when he received a long pass on the edge of the area but his shot flashed wide shortly before Mazyar Zare’s effort went over the crossbar.
The best chance for Al Shabab in the second-half came after 76 minutes when Abdullah Shuhail broke down the left before sending a cross into the area that was headed onto the bar by Sanad Shrahilee.
Al Shabab came close again with 11 minutes remaining when Nassir Al Shamrani received a cross from the right before striking a powerful volley that was denied by Memarzadeh with the aid of the left upright.