Franco was on the scoresheet
Antonio Naelson posted the third goal for the Latin Americans while Yahya Golmohammadi scored Iran's only goal.
The victory placed Mexico in first spot of Group D and Iran remain pointless in the bottom of the table before Portugal and Angola clash late on Sunday.
Iran started brighter and they came close to breaking the deadlock in the 11th minute when Mehdi Mahdavikia raced down the right but Vahid Hashemian couldn't connect with his low cross.
Shortly after, Hashemian himself saw his header brilliantly saved by Oswaldo Sanchez to deny Iran from taking the lead.
But it was Mexico who took the lead in the 28th minute against the run of the play when three players combined for the first goal.
Guillermo Franco headed a Pavel Pardo free-kick into the path of Bravo who easily slotted the ball into the back of the Iranian net.
Iran pushed for an equalizer and they found it when Hashemian's strong header from was blocked by Sanchez only for Golmohammadi to flick into the empty net.
Mexico coach Ricardo La Volpe started the second half by bringing in Luis Perez and Naelson and Ricardo Torrado in an attempt to restore the lead.
Mexico had most of the possession and kept Iran in their own half but without any real danger on the Iranian defense until the middle of the second period when they netted almost back-to-back goals.
In the 74th minute, Mexico benefited from a string of howlers from Iranian keeper and defense before Naelson released Bravo to burry the ball home.
Pardo was released by a magic pass from Bravo before swinging an inch-perfect cross for Naelson to head Mexico's third from close range.
Mexico will face Angola in their second game on June 16th while Iran are set to Portugal one day after.
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