Saber Kazemi earned 18 points for Iran and Mikhaylov Maxim scored 22 points for the Russians.
Iran had lost to Japan 3-0 in the opening day of the competition.
Team Mell will meet Netherlands on Sunday.
The competition format is a single round robin pool with each of the 16 teams facing every other ahead of semifinals between the top four of the standings.
The semifinal winners will clash for the title, with the losers playing out for the bronze medal.
The tournament is being held in Rimini, Italy within a secure 'bubble' with all hygiene protocols in place to ensure the health and well-being of all athletes, officials and staff throughout the competition.