Mehdi Shirmohammadi, Reza Dayeri and Sobhan Faleh scored for Iran.
Team Melli had started the campaign with a 3-1 win over Azerbaijan.
Iran will meet Belarus in its last match in Group B.
Russia, Uzbekistan, Oman and Egypt are in Group A.
The 2nd CIS Games are being held in Belarus from August 4 to 14.
The CIS Games are a regular complex event in the field of physical culture and sports, covering national sports, the most popular within the CIS member states, Olympic and non-Olympic sports.