A state television report in Iran showed the Boeing-727, which carried 69 passengers including Iraqi civil aviation officials and reporters, landing and taxiing to the terminal.
The flight later returned to Baghdad.
Sunday's flight carried journalists and politicians rather than fare-paying passengers and was intended as an advertisement for the forthcoming scheduled flights, Iraqi airline sources said.
Regular flights between Baghdad and Tehran - on Wednesdays and Fridays - were expected to resume on November 16, the report said.
The flights are evidence of growing reconciliation between Iran and Iraq, which fought a bloody war from 1980-88 that left about 1 million dead on each side.
When border disputes soured Iran-Iraq bilateral relations in 1980, both countries stopped their flights to each other.
Iran has worked to rebuild relations with Iraq since the fall of ex-Iraqi dictator Saddam Hussein in 2003.
The television report said Iraq would provide security to Iranian airlines that plan to resume flights to Iraq.
Iraq's national carrier is now also flying to Syria, Jordan, United Arab Emirates and Turkey, and plans services to Lebanon.
Iran and Iraq have already begun some commercial exchanges trading in oil products and flour.