Argentina coach Alejandro Sabella called Lionel Messi "a genius" after his stoppage-time goal beat Iran and put his side into the knockout phase.
Iran had frustrated Argentina with a solid defensive display until Barcelona forward Messi curled in his second goal of the World Cup.
"We have a genius who is called Messi and fortunately he is Argentine," said Sabella.
"Iran made life hard for us but with Messi, everything is possible."
Messi had scored just once in eight World Cup finals appearances before this tournament, and ended an eight-year wait for a goal in the opening 2-1 win over Bosnia-Hercegovina.
Again the 26-year-old was not at his best but found space in the 91st minute to bend a brilliant left-footed strike into the far corner, his 40th goal for his country.
"There are many things we have to think about and improve," said former Sheffield United and Leeds player Sabella, 59. "In the first half, Iran had four or five clear chances to score.
"All players who played today have contributed to this victory but of course we have a genius who is called Messi. Not even two goalkeepers could have stopped that Lionel shot."
Two-time World Cup winners Argentina were strong favourites to beat Iran but Sabella's side struggled to create chances.
In fact, Iran had the two best openings, with Charlton's Reza Ghoochannejhad and Fulham winger Ashkan Dejagah forcing Sergio Romero into flying saves.
And Dejagah was adamant that he should have had a penalty after tumbling under a Pablo Zabaleta challenge.
Iran coach Carlos Queiroz said: "At the end, two personalities in the game made the difference. The number one was the referee. The second was Lionel Messi.
"I hope they don't punish me, but I'm telling the truth: it was a penalty.
"It should have been a penalty and red card. There's no excuse. There's nothing that can explain [why] this Serbian referee [did] not give the penalty.
"How can this guy sleep tonight, or for the rest of his life? With all respect, I would like to have the opportunity to have a one-on-one conversation with him. Why did he do that to us?"
Iranian President Hassan Rouhani praised the effort of Queiroz's team, who can still qualify from Group F.
"The passionate youth of the Islamic Iran have shown their determination and capabilities to the world again," he said in a statement.
"I would like to thank the assiduous players of the national team and coaching team who delighted the hearts of the nation and surprised everyone with their fair and enthusiastic play against the national football team of Argentina."
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