It was Iran’s first victory in the competition as the Asian powerhouse has lost to Argentina and Poland in its two previous matches.
Seyed Mohammad Mousavi, who collected eight blocks in the loss to Poland in five sets on Tuesday, came back to record five more among his 12 points against Cuba.
Shahram Mahmoudi enjoyed a good overall performance with 19 points, including three blocks, to lead the Iranian side, and Adel Gholami chipped in with 11, including three blocks, in the victory.
Miguel Lopez finished as the Cuban top scorer with 15 points and Osniel Melgarejo added 14 in the loss.
Iran has been scheduled to meet Egypt on Saturday.