Eamon Zayed, Mehrdad Pouladi and Hossein Badamaki all netted as the Iranian outfit came from behind to seal their passage into the Round of 16
Al Shabab defender Issa Mohammed had fired the hosts into a shock early lead, but Persepolis eventually fought back after Ireland-born Eamon Zayed pulled a goal back before half-time, with further strikes in the second 45 winning the day.
The result confirmed the Reds' place in the last 16 of the ACL much to the delight of the healthy visiting contingent of Iranian fans, with top spot in the group a possibility with Al Hilal needing to win at home to Al Gharafa later in the evening to deny them.
Earlier, the Dubai outfit had gone ahead on eight minutes when veteran defender Mohammed produced a powerful long-range strike which got past a non-existent Persepolis wall and swerved beyond keeper Asmir Avdukic.
Persepolis skipper Ali Karimi tried to respond with a 27th-minute header going just wide, while moments later he teed up Gholamreza Rezaei whose effort forced a good save from Al Shabab keeper Ismail Rabee.
The breakthrough would come on 43 minutes when Karimi picked out the unmarked Zayed at the back post and the Libya international headed past Rabee for the leveller.
The impressive Mehrdad Pouladi had a good penalty shout turned down early in the second 45 when Hamdan Qassim, fresh from a booking, appeared to bring him down inside the box.
However, moments later Pouladi was celebrating when he fired home a fine left-foot free-kick in off the post to make it 2-1.
Zayed almost added a third on 55 minutes, when his powerful shot proved too much for Rabee but not the crossbar as it agonisingly bounced off the woodwork and away from goal.
On 64 minutes, Al Shabab almost produced a shock response when Mohammed glanced a header wide from a free-kick, but the visitors soon firmly re-established control.
Zayed dragged an effort wide, while Pouladi forced a good save from Rabee, before substitute Hossein Badamaki produced some wonderful skill to beat two defenders inside the box and went on to finish sublimely to round out the scoring in the 90th minute.