A poor game which had been marred by security and crowd issues, forcing a 82-minute delay, was decided by a quality finish from Martinez -- his fifth goal of the tournament.
The win was the third straight major tournament title for Argentine following their 2021 Copa victory and their triumph in the 2022 World Cup in Qatar.
There were tears before the celebrations though with Argentina captain Lionel Messi going off injured in the 66th minute watching the rest of the game distraught on the bench, while there was an emotional farewell for Angel Di Maria in his final game for the national team.
For Colombia, whose only title came in the 2001 Copa America, it was a disappointing night when little seemed to work for Nestor Lorenzo's team.
There was chaos around entry to the stadium for fans, with organisers blaming supporters for trying to enter without tickets while fans blamed the lack of an efficient entry system to the venue.
The scenes were alarming with some fans needing medical attention for heat exhaustion but after the decision to suddenly throw open the gates, with no checks on those entering, the situation was largely resolved and the game finally went ahead.
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