Hadadifar's free-kick 57 minutes into the first-leg encounter settled the contest in the Iranians' favour and extend Al Hilal's away-day misery in this season's competition.
But last year's Saudi double-winners will rue a penalty miss just before the interval which would have given them a crucial away goal.
Zob Ahan had the better of a lively first-half, creating a number of chances through Brazilian striker Igor Castro and Iranian international Mohammad Reza Khalatbari, who thought he should have been awarded a spot kick in the first minute.
Castro then beat the Al Hilal defence in the air but his header from eight yards out was well saved by keeper Hasan Al Otaibi.
With 23 minutes gone and Zob Ahan constantly threatening the visitors with their pace, Castro showed great technique to bring down a high ball and create space for himself but his shot was blocked by Osama Hawsawi.
Zob Ahan right-back Mohammad Hoseini nearly scored his sixth goal of the season on the half-hour mark when he ghosted in at the far post but could only send a deep corner wide of the goal with his shin.
Al Hilal, who had briefly threatened through captain Nawaf Al Abid in the opening stages and a deflected Ahmed Al Fraidi shot that was saved, then had a golden chance to take the lead after 41 minutes.
Saudi Arabia striker Yasser Al Qahtani was brought down in the area by Mohammad Ali Ahmadi as he was about to attempt a delicate lob over onrushing Zob Ahan goalkeeper Shahab Gordan.
However, Swedish midfielder Christian Wilhelmsson struck the penalty at a comfortable height for Gordan, who did not have to move far to save it.
Wilhelmsson also played a part in Zob Ahan's goal 12 minutes after the break.
Hadadifar stepped up and hit a low free-kick which flew through the gap left in the Al Hilal wall by the Swede, who had turned away, and beyond an unsighted Al Otaibi.
The goal galvanised the visitors, who hit the woodwork through Al Abid in the 70th minute.
The skipper twisted and turned his way into the Zob Ahan box before hitting the outside of the post with a powerful left-foot shot.
Al Abid could have snatched a draw in stoppage time when he tried to get on the end of Al Fraidi's superb cross but Hoseini somehow managed to distract the midfielder as the Iranians held on.