Team Melli lost the first set 25-20 but beat its strong rival in the next three sets with the same score of 25-23.
Amir Ghafour led Iran with 20 points and Italian Gabriele Nelli also scored 20 points.
Iran will face host China on Saturday in Pool 1 and play Germany on Sunday.
The 2019 FIVB Volleyball Men's Nations League is the second edition of the FIVB Volleyball Men's Nations League, an annual international men's volleyball tournament contested by 16 national teams.
The competition will be held between May and July 2019 and the final round will take place in the Credit Union 1 Arena, Chicago, United States.
This is the first edition of the World League or the Nations League to have the Final Round hosted in North America.