Alsu Abdullina (28th minute), Anna Belomytseva (38th minute, penalty kick), Valeria Bizenkova (42th minute) and Natalia Mashina (83th minute) scored for Russia.
It was the first ever meeting between the Russian and Iranian women’s football teams.
They are scheduled to play again on July 18.
That match will be played without spectators in Novogorsk outside Moscow.