The Iranian wrestlers won three bronze medals and came second with 36 points.
Mohammadali Geraei at 71kg, Saeid Abdvali at 75kg and Hossein Nouri at 85kg won three bronze medals in the competition.
Russia won the title with 46 points after claiming two silver and two bronze medals.
Turkey came third with 34 points. It finished day two at the summit of the medals table with two golds and a bronze.
Team Rankings (Top Six)
1. Russia, 46 points (0 gold medal, 2 silver, 2 bronze)
2. Iran, 36 (0-0-3)
3. Turkey, 34 (2-0-1)
4. Georgia, 30 (0-0-2)
5. Germany, 29 (1-1-1)
6. Armenia, 28 (2-0-0)