A World Cup played out uneasily in a country under the grip of a brutal military dictatorship culminated in the hosts beating the Dutch 3-1 after extra time in the hostile environment of the Monumental Stadium, with Mario Kempes scoring twice.
For the Dutch, it was a second consecutive final defeat, after their 2-1 loss to West Germany in 1974, but no European side has come so close to winning the World Cup in South America.
Kempes put Argentina ahead, but substitute Dick Nanninga equalised and Rensenbrink then hit the post in the dying seconds for the Dutch.
It was an agonising miss, and Argentina took full advantage to secure their first World Cup in extra time as tournament top scorer Kempes netted again before Daniel Bertoni added another.
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The result left a bitter taste in the visitors' mouth, as they claimed they were unsettled when the Argentines stalled the start of the match by complaining about a plaster cast on Rene van de Kerkhof's wrist.
Krol also said the Argentines had pressured FIFA into selecting Italy's Sergio Gonella to referee the match. And that was not the only claim made that the hosts, perhaps with the influence of dictator Jorge Videla's military government, had manipulated their way to final victory.
Indeed, in their final game of the second group stage, Argentina knew they needed to beat Peru by four clear goals to pip Brazil to a place in the final. In the end, they put six unanswered goals past Peru's Argentine-born goalkeeper Ramon Quiroga.