Mohammad Banna's men beat Turkey 4-3, with Faghiri (55 Kg), Norouzi (60 Kg), Abdoli (66 Kg), and Akbari (96 Kg) giving Iran wins over their Turkish rivals.
Iran's win is remarkable as the star of the team, Hamid Sourian, was missing the competition.
Iran overpowered Cuba in the team's opening round and overpowered a Nordic team composed of Swedish and Danish wrestlers in its second encounter.
It then beat the hosts, Armenia, 4-3 in a closely fought semi-final.
A total of eight teams (Georgia, Turkey, Russia, Hungary, Iran, Cuba and a Nordic team) took part in the 2010 Greco-Roman Wrestling World Cup, held in Yerevan, Armenia, from February 12-14.