Amini broke the deadlock seven minutes before the break with a powerful strike and Bulut tapped in the second in the 59th minute before Antonis' late goal added the gloss to a second consecutive Group A victory for the Young Socceroos, who had Marc Warren dismissed in stoppage time.
Iran skipper Payam Sadeghian missed a penalty in the second-half as Iran slumped to their second defeat of the tournament.
A low-key opening 45 minutes saw defences on top. Jahan Jahanbakhsh's weak shot from distance was comfortably gathered by Mark Birighitti and Omid Alishah's header following Saeid Lotfi's cross was straight at the Australian keeper.
Yaghoub Karimi failed to extend Birighitti from 30 yards before Australia took the lead in the 38th minute.
Warren's corner from the right was only cleared as far as Amin on the edge of the box and the midfielder hammered a shot into the top corner.
Milad Gharibi's free-kick from a promising position was off target four minutes into the second-half before Australia extended their lead just before the hour mark.
Matthew Leckie's superb pass split the Iranian defence and set Tommy Oar free down the left. Ben Kantarovski met the substitute's cross with a firm header that keeper Ali Reza Safarbeiranvand did well to tip onto the bar but Bulut was on hand to knock in the rebound.
Iran almost provided an instant response but Birighitti pushed Kaveh Rezaei's well-struck effort from 20 yards around the post before they were gifted a golden opportunity to get back into the game in the 71st minute.
Birighitti came out to deal with a fairly routine through ball but slipped and fell as he turned, presenting Rezaei with a clear run at an empty goal.
However, the Australian keeper stretched out an arm to bring down the Iran forward and the referee pointed to the spot. Payam Sadeghian's well-struck penalty sent Birighitti the wrong way but came back off the left post.
A nervous few minutes followed for Australia as Sadeghian and Rezaei both saw shots held by Birighitti and the keeper managed to stop Karimi's deflected effort before Antonis netted the third goal three minutes from the end as Safarbeiranvand could not keep out the substitute's low shot from 20 yards.
However, Warren's dismissal in stoppage time following a clash with Mojtaba Mahboub saw the game end on a sour note for Australia.