Iliya Petkov collected 20 points for Bulgaria, and Amin Esmaeilnezhad led Iran with 16 points.
Iran had lost to Japan 3-0 and Brazil 3-1 in its first two matches.
Team Melli is to face Turkey on Saturday.
The VNL Preliminary Phase features three competition weeks per gender, with each of the 16 teams playing 12 matches.
The seven best-ranked national teams in the Preliminary Phase will join hosts Poland for the Finals, which will be held in Lodz from June 27 to 30.