Afshin Ghotbi’s charges travelled to Slovenia from their training camp in Austria for the game but were trailing four minutes from half time following a Milan Vilotic strike.
Former AFC Player of the Year Ali Karimi restored the parity three minutes later from the spot.
Red Star Belgrade dominated the first half while Team Melli had the upper hand after the break but they failed to score the winner.
Iran, who were drawn with defending champions Iraq, DPR Korea and UAE in the continental showpiece, will play Hungarian side Vasas on July 17 and Italian outfit Lazio on July 21.
Red Star Belgrade:
Stamenkovic, Ninkov, Vilotic, Djordjevic(capt), Tosic (Reljic), Cadu, Bogdanovic, Jevtic (Subasic), Perovic, Koroman (Vesovic)
Iran:
Mehdi Rahmati, Hadi Aghili, Jalal Hosseini, Khosrow Heidari, Pejman Nouri, Ali Karimi (68 - Mobaly), Farzad Ashobi, Ehsan Haj Safi (68 - Mohammad Nosrati), Karim Ansari Fard (65 - Meydavoodi), Zenyedpour ( 60 - MR Khalatbari), Mehrzad Madanchi (46 - Gholamreza Rezaei)