Ghasem Dehnavi gave a lead to Iran in the 31st minute and two minutes later Karim Ansarifard scored another goal.
Mauritania is 202nd in the FIFA world rankings released last week.
The Persians will also host the Mozambique national team in Tehran's Azadi stadium on May 2.
Iran is gearing up for the final stage of Asian qualifying for the 2014 World Cup.
Carlos Queiroz’s team has been grouped with South Korea, Uzbekistan, Lebanon and Qatar in the competition.
Iran - Mauretania 2-0 (2-0)
Inofficial friendly match, Azadi stadium, 200 spectators
Goals:
1-0 Ghasem Dehnavi (31' / assist by Ehsan Hajsafi)
2-0 Karim Ansarifard (33' / Hajsafi)
Iran first half: Forouzan - Mahini, Khalilazadeh, Amir-Hossein Sadeghi, Hajsafi - Hadadifar, Dehnavi, Zanidpour - Yaghoub Karimi, Gholami, Ansarifard
Iran second half: Gordan - Fakhredini, Kouroshi, Ebrahim Karimi, Akbar Sadeghi- Reza Haghighi, P. Nouri, Mosalman - Sadeghian, Ghazi, Hassanzadeh