Iran will now travel to Kochi for the quarter-final tie with Spain, who scored the last-minute winner in their pre- quarterfinals against France in Guwahati.
Iran exploited the rival's weak defence to score through Mohammed Sharifi (7th) and Allahyar Sayyad (11th).
Mexico though attacked from the word go and created several chances, they were either off the target or failed to surpass the rival keeper Ali Gholam Zadeh.
However, Mexico managed to reduce the margin in the 37th minute through Roberto De la Rosa.
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Each time Iran's defence fell apart, it was keeper Zadeh who came up with some smart saves, especially in the second half, to deny the Americans a chance to score goals.
Iran, knowing that Mexico are good in the attack, adopted a cautious approach to keep their rivals attacking moves at bay and waited for opportunities to punish Mexico's weak defence.
Iran earned a penalty in the 7th minute when Mexico defender Adrian Vazquez brought down Mohammed Ghaderi while going for the ball inside the box and referee Anthony Taylor had no hesitation in awarding the penalty, which Sharifi converted successfully.
Unfazed by the set back, Mexico kept on attacking with a series of moves and after missing couple of close chances, they managed to find the net.
Roberto De la Rosa found the back of the net off a rebound from the top of the box after the Iranian keeper managed to block Diego Lainez's left-footed shot. Daniel Lopez, who was the livewire in the middle, initiated the move.
The second half was more lively as both the teams went on the attacking mode and both the goalkeepers made some good saves.
Iran also had their share of exchanges and scoring chances but could not breach keeper Lopez as he came out of his charge twice to block Younes Delfi and Sayyad's shots from close.
Mexico could have scored another goal but luck was not on their side as Jairo Torres' shot from a difficult angle off a free kick hit the left post.
Iran's Younes Delfi, who received a yellow in the 80th minute, the second in the tournament for rough tackle, will miss the quarterfinal match against Spain.