Iran came from 2-1 behind to beat the African powerhouse 5-3 in Group B.
Amir Hossein Akbari (three goals), Mostafa Kiani and Mohammad Masoumizadeh were on target for Iran.
Moustafa Samir, Adbelrahman Hassan Ahmed and Moustafa Aly Mohamed scored for Egypt.
Team Melli defeated Mexico 7-4 on Tuesday and then faced Russia on Thursday to decide the table topper.
The 2019 Beach Soccer Intercontinental Cup is the eighth edition of the Beach Soccer Intercontinental Cup, an annual international beach soccer tournament contested by men's national teams.
The competition is being held in Dubai, the UAE between 5 and 9 November.