Mohammad Mohebi was on target in the 14th minute.
The match was held at the Hristo Botev Stadium in Plovdiv, the second-largest city in Bulgaria.
Team Melli is scheduled to face Angola in Tehran on September 12.
Iran prepares for the 2023 AFC Asian Cup, which will be held in Doha, Qatar from January 12 to February 10, 2024.
Iran is drawn in Group C along with the United Arab Emirates, Hong Kong China, and Palestine.