Late goals from Omar Bravo and Antonio Zinha handed Mexico a comfortable victory in Nuremberg.
Mexico took the lead from a free-kick which was flicked on by Guillermo Franco leaving Bravo a simple tap-in.
Iran drew level when Yahya Golmohammadi pounced on a loose ball after a flap by goalkeeper Oswaldo Sanchez.
But Rahman Rezaei's dithering on the ball allowed Zinha to play in Bravo, who tucked away Mexico's second before Zinha turned scorer with a free header.
The result means Iran fail to improve on their record of only one victory in the World Cup.
But seasoned tournament competitors Mexico extended their record of no defeats in their last nine group-stage matches.
Both sides looked at ease in the searing heat and Iran's quick passing in midfield suggested they were not overawed by the occasion.
And it was the Iranians who had the first chance to open the scoring when Vahid Hashemian headed on target forcing Sanchez into a fine save low down.
Marquez and Franco both threatened with headers from corners as Mexico began to get a foothold in the match.
And it was the Mexicans' aerial superiority from set-pieces that was Iran's undoing on 28 minutes.
Pavel Pardo's free-kick was flicked goalwards by Franco, leaving Bravo to tap-in from five yards.
But Iran were quick to respond with a set-piece goal of their own.
Rahman Rezaei's header was blocked by Sanchez after Mehdi Mahdavikia's corner, but Golmohammadi reacted quickest among a group of players to poke home.
Iran deserved to go into the break level and it was Mexico coach Ricardo Lavolpe who decided to alter his line-up at half-time.
And after Jared Borgetti's injury on 50 minutes, Lavolpe had used all three substitutes.
Mexico has a strong shout for a penalty turned down when Marquez was clattered by Golmohammadi after a flowing move down the Mexico right.
And it was the Mexicans who bossed possession in the second half with Iran unable to find the intensity that served them well in the first period.
The tired Iranians eventually faltered and Mexico killed off the game in three minutes.
Rezaei's error on the ball allowed Zinha to slip a perfect pass to the feet of Bravo, who coolly slotted home on 76 minutes.
Zinha then netted one for himself by powering home Mario Mendez's right-wing cross with a bullet header.
Mexico have won four of their last five opening matches at a World Cup. Iran scored for the first time ever in an opening fixture at the World Cup finals.
Mexico are unbeaten in their last 13 group phase matches at World Cups. The last team to defeat them in a group stages was Norway in 1994.
Brazilian born Mexico midfielder Zinha became the second player this World Cup to score for a country in which he was not born. German striker Miroslav Klose, born in Poland, was the first. Yahya Golmohammadi became the ninth oldest player to score at the World Cup at an age of 35 years and 84 days. Ali Daei became the oldest ever Iran player to participate in the World Cup at an age of 37 years and 82 days. Indeed Iran fielded their oldest ever starting line-up. The average age in their seventh ever World Cup match was 28 days and 133 days.