Manchester United's record British signing Angel Di Maria scored once and made goals for Sergio Aguero, Erik Lamela and Federico Fernandez as Argentina won their first game since losing to Germany in Brazil.
Andre Schuerrle and Mario Goetze replied but Germany were brought crashing down to earth by a ruthless Argentina display in what was Gerardo Martino's first match in charge of the South Americans.
Martino, who filled the vacuum left when Alejandro Sabella declined the offer of a new contract after the World Cup, said the victory should not be over-hyped.
"That's not easy to try to find a new team. Di Maria was more prominent than he was in the World Cup."
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His German counterpart Joachim Loew refuted suggestions that Argentina had avenged the defeat in the final.
"It can't be revenge. You can't repeat the final. I can't actually fault the team because they have never played like that together before. Some players aren't in form," said Loew.
Before kick-off the home fans got a chance to say a final farewell to Arsenal defender Per Mertesacker, record goal scorer Miroslav Klose and World Cup-winning captain Philipp Lahm.
All three retired from international football after Germany's success in Brazil.
Only four players who started the World Cup final were in the German line-up, with Manuel Neuer captaining the side in the absence of his injured Bayern Munich teammate Bastian Schweinsteiger.