The winger - who moved to Manchester United last week in a British record £59.7 million deal - stole the show in Dusseldorf on Wednesday, creating three and scoring one himself in a comprehensive 4-2 win.
The friendly victory - which came courtesy of strikes from Sergio Aguero, Erik Lamela and Federico Fernandez, as well as Di Maria's 50th-minute chip - ultimately did little to erase the painful memories of the South Americans' World Cup final defeat to the same opponents back in July, but it did at least provide a stage for the 26-year-old to showcase his considerable talent.
"Angel di Maria has demonstrated why he is one of the five best players in the world," said Martino afterwards, before going on to praise the entire Argentina team.
In a game that they dominated for long periods, the visitors' victory was made all the more impressive given they were shorn of the talents of several star names - with the likes of Ezequiel Garay, Gonzalo Higuain and talisman Lionel Messi all missing through injury.
And that was enough to give former Barcelona coach Martino a timely boost as he began his tenure in charge of the national team with a high-profile win.
"I am very satisfied with the performance of my team because we had a few players left who have not had as much match practice," he added.
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