However, as the match entered added-on time, Messi strode forward before curling the ball into the top corner from 25 yards to earn his team a place in the second round.
Below, Sports Mole assesses whether Argentina were deserving of the three points in Belo Horizonte.
On target: 4
On target: 3
Was the result fair?
When you take into consideration the amount of chances created and the possession of the ball, you have to say that Argentina probably deserved to win this game, but certainly not in the circumstances that transpired. Iran gave everything, and while a heavy defeat looked on the cards before the game, they could have very easily won this game by a couple of goals and Argentina could have had no complaints. Messi's goal was sublime, though, and worthy of winning matches more significant than a group game at a World Cup.
Coach Alejandro Sabella would have come away from the win against Bosnia-Herzegovina encouraged that he had found the right formation for his side, but it was another poor showing from Argentina and their boss will have genuine concerns that they are going to fail to reach the latter stages. They were indebted to two excellent stops from Sergio Romero to keep them level, and like in the first game, if it wasn't for the brilliance of Messi, they wouldn't have won this football match.
There aren't enough words that can do the performance of Iran any justice. After all of the flak that they received for their contribution to the 0-0 draw against Nigeria, they responded with the grittiest of displays that deserved so much more than they got. The goalkeeper and back four were immense, captain Andranik Teymourian kept a grip on things in the middle while the attacking flair of Dejagah and Ghoochannejhad ensured that the Argentina defence never had a moments peace. Manager Carlos Queiroz will have to pick up a deflated dressing room, but the minnows can be proud of the way that they competed against one of the world's elite.
Sports Mole's man of the match
Ashkan Dejagah: This could very easily go to Lionel Messi who, at the end of the day, was the pivotal factor, but Ashkan Dejagah delivered a performance that saw him get the better of Pablo Zabaleta, and it's not every day that someone can do that. Time after time, he attacked the full-back, and he should have won a penalty after displaying his superior speed against Zabaleta in the corner of the area. The Fulham winger can also count himself unfortunate not to get on the scoresheet after Romero pulled off a one-handed stop to prevent his header hitting the back of the net.
We will get onto one of the biggest gaffes of the night in the following section, but both Hosseini and Ghoochannejhad will be ruing the opportunities that they squandered. Hosseini's header at the end of the first half was from no more than six yards out, while Ghoochannejhad should have converted the ball into the corner of the net after being found with a right-wing corss.
It was a strong performance from Milorad Mazic but his night will be remembered for his failure to award a penalty to Iran during the second half. Dejagah was taken down by a stray leg from Zabaleta, but Mazic wrongly thought that the Manchester City full-back had taken the ball, and by the final whistle, it was a decision that ultimately cost Iran.
Argentina: Argentina end the group campaign with a match against Nigeria.
Iran: Iran must beat Bosnia-Herzegovina in their final group match to have any chance of securing a place in the second round.