With both sides cancelling each other out, the game called for a moment of ingenuity and it came in the form of Fatemeh Lotfzadeh who surged into the Saudi Arabia box only to be brought down with Yasna Jarfarnia converting past Dima Shaikh for the opener.
Tania Ghorbani doubled the advantage to seal a 2-0 win for the Persians.
Saudi Arabia were given a lifeline in the 68th minute when Iran goalkeeper Elina Shahbazi handled the ball outside of her box and was shown the red card but despite the numerical advantage, was unable to salvage anything from the game.
Next up for Iran is Kuwait on Wednesday while Saudi Arabia faces another test in the shape of an impressive Lebanon.