The winger scored one goal and created three others, for Sergio Aguero, Erik Lamela and Federico Fernandez, before Andre Schurrle and Mario Gotze replied for the stunned hosts
The winger, who joined Manchester United for a British record transfer fee of €84 million last week, stole the show with an outstanding performance in the World Cup final re-match, giving fans of the Premier League club plenty of reason for cheer.
And while a friendly win – even one as resounding as this – did little to avenge their heartbreak in Brazil, Argentina could at least take heart from the fact that they ruined Germany's homecoming party at the Esprit Arena.
Di Maria missed the World Cup final through injury, as Mario Gotze's extra-time goal settled matters in Rio de Janeiro and gave Germany their fourth success on football's grandest stage.
But the former Real Madrid attacker gave Germany left-back Eric Durm a torrid time on this occasion and set up Argentina's first three goals, scored by Sergio Aguero, Erik Lamela and Federico Fernandez respectively.
Di Maria then got in on the act himself, extending their lead with an exquisite 50th-minute chip over Germany substitute Roman Weidenfeller, meaning Andre Schurrle's quick response and Gotze's deflected 78th-minute strike were no more than consolations for a Germany side who saw Mario Gomez miss a host of first-half chances.
Now retired from international duty, World Cup heroes Philipp Lahm, Miroslav Klose and Per Mertesacker were presented to the crowd before kick-off, but the trophy was not out of respect to Argentina.
New Germany captain Bastian Schweinsteiger and defenders Mats Hummels and Jerome Boateng missed out through injury, while Argentina were also without several stars - Lionel Messi, Ezequiel Garay and Gonzalo Higuain all sidelined.
Gomez, leading the Germany line in the absence of Klose, missed a great chance to open the scoring when he was played through in the seventh minute, with the 29-year-old shooting straight at Sergio Romero.
At the other end, Di Maria looked lively and, having fired over, he then set up Aguero for the game's first goal after 20 minutes.
Di Maria produced a superb cross with the outside of his left foot and Aguero did the rest, coolly volleying past Manuel Neuer from five yards.
Germany should have levelled when Gomez got on the end of a neat move that involved Christoph Kramer and Marco Reus, but the striker - again one-on-one with Romero - was denied by the goalkeeper's trailing leg.
Argentina ramped up the pressure from there as the increasingly dominant Di Maria tested Neuer, while Aguero shot just wide twice and the substitution of Julian Draxler, taken off with a hamstring niggle, added to the visitors' momentum.
Lamela then struck five minutes before half-time, cushioning a first-time volley into the top corner in stunning fashion after Di Maria had found him from the byline.
Germany's plight was summed up by Gomez screwing an effort wide when Romero spilled Reus' shot on the stroke of half-time and they found themselves three goals down in the 47th minute when Di Maria picked out Fernandez at the back post with an excellent free-kick.
Weidenfeller, who replaced Neuer at half-time, should have come for the ball but instead was reduced to the role of spectator as the Swansea City man rose above Matthias Ginter to score from close range.
And Di Maria quickly made it four, storming past Ginter to latch onto Pablo Zabaleta's throughball before lifting an effort over Weidenfeller.
Schurrle responded in the 52nd minute, tapping in the rebound after he had initially volleyed straight at Romero, and Reus hit the post as Germany looked to restore some pride.
Gotze's goal - which took a wicked deflection off Fernandez - reduced the margin further with 12 minutes to play.
It was not to be Germany's night, though, as Di Maria stole the headlines with a superb solo performance.