In the 105kg weight category, Barari finished third in the snatch with 180kg before winning the clean and jerk with 221kg.
Mohammad Reza Barari claimed the gold medal with a total of 401kg.
Ivan Efremov from Uzbekistan snatched the silver with a total of 394kg and his countryman Sardorbek Dusmurotov won the bronze medal with 386kg.
Iran’s Ayoub Mousavi in the 85kg and Ali Hashemi in the 94kg had already won two silver medals in the event.
The tournament, which will run until April 30, has brought a total of 161 lifters from 30 countries together in Tashkent, Uzbekistan and serves as a qualification event for the Olympics.