Wahbi Khazri proved the talisman for the home side and it was his dribbling run that led to the 71st minute winner. Khazri's shot was parried by Iran goalkeeper Alireza Beiranvand into the path of defender Milad Mohammadi, who could only turn the ball into his own net.
Tunisia, who share the same World Cup group with Belgium, England and Panama, might have had a second soon after but Khazri's powerful close range effort was well saved.
Iran were using the match to approximate the playing style of Morocco, who share their group in Russia with Portugal and Spain.
A dipping free kick from captain Ehsan Hajsafi in the 67th minute, saved by Tunisia's Farouk Ben Mustapha, was the closest Iran came to scoring.
Tunisia next meet another fellow World Cup qualifier Costa Rica in Nice, France on Tuesday while Iran take another north African country, Algeria, in Graz, Austria the same day.
(Reporting by Mark Gleeson in Cape Town; Editing by Christian Radnedge)
