Ali Shafiei led Iran with 20 points, while Cuban Osniel Lazaro Mergarejo Hernandez registered 15 points.
Host Russia also defeated Mexico 3-0 (25-15, 25-11, 25-17) in St. Petersburg.
Iran will play Mexico and Russia on Saturday and Sunday, respectively.
A group of 24 teams are competing for six available tickets to Tokyo 2020.
The teams are divided into six pools of four, with the table toppers punching their tickets for next year’s Olympic Games.