Russia captain Dmitriy Muserskiy tallied 20 points, including 16 kills, one block and three aces; and Maxim Mikhaylov added 10 more points for the Russian team.
Iran’s Amir Ghafour and Mojtaba Mirzajanpour finished the match with 12 points each. Iran suffered with 27 turnovers that allowed Russia to build a good lead in crucial moments of the match.
Iran has been scheduled to face Italy on Thursday.
The tournament is a qualification process for the 2016 Summer Olympics in Rio de Janeiro, Brazil.
The top two teams will qualify for the Olympics and join Brazil as it has already secured a berth as the host country.
The 2015 FIVB Volleyball Men’s World Cup began on September 8 in Japan and will finish on September 23.