The £59.7million Manchester United signing created three goals and scored one as the South American giants avoided a repeat of their World Cup final defeat at the hands of Germany.
Di Maria was injured for that match at the Maracana in Rio de Janeiro which Germany won 1-0 after extra-time, but he was at his best against Die Mannschaft in Dusseldorf.
Argentina were without their star player Lionel Messi due to injury for Wednesday’s encounter, but coach Gerardo Martino’s starting line-up still had some top players, including Di Maria, Sergio Aguero, Javier Mascherano and Pablo Zabaleta.
Meanwhile, Germany coach Joachim Low left some of his World Cup stars such as Mesut Ozil, Mats Hummels, Thomas Muller and Mario Gotze on the substitutes’ bench, but his starting line-up was still strong with Marco Reus and Toni Kroos both present.
Both Germany and Argentina started the game well, but it was the hosts who had the first chance of the match in the seventh minute.
New Real Madrid signing Toni Kroos created the opportunity with a lovely ball to send Mario Gomez through on goal, but the Fiorentina striker’s shot was saved by Argentina goalkeeper Sergio Romero.
Di Maria could have punished the Germans for that miss when he took an attempt on goal from the edge of the box, but his left-footed volley went just over the crossbar.
The 26-year-old winger was causing all sorts of problems for Germany down the right-hand side and was the architect of the visitors’ opening goal on 20 minutes.
The former Real Madrid star delivered a perfect cross with the outside of his left foot that Manchester City forward Sergio Aguero tapped in from just yards out.
However, Argentina could have conceded the equaliser just three minutes later had Kroos’ powerful shot from just outside the box not narrowly gone wide.
The South American giants continued to press forward, though, as Erik Lamela forced Manuel Neuer into making a good save from a narrow angle, before Gomez failed to get the better of Romero after being wonderfully teed up by Reus in a very good position.
Di Maria was the best player on the pitch in the first half and could have scored Argentina’s second goal on the half-hour mark.
The former Benfica player galloped down the right, skipped past a challenge and then shot on goal, but his attempt was too weak to trouble Neuer.
Argentina did not have to wait long for their second goal, though, and Di Maria was once again at the heart of it.
The former Real Madrid attacker floated in a brilliant cross from the right that Tottenham Hotspur winger Lamela turned in with a sensational first-time cushioned volley from inside the Germany box.
Four-time world champions Germany, who were looking threatening before they conceded the second goal, could have pulled one back just before the half-time interval.
Reus tested Romero with a powerful shot from outside the box and the rebound fell to Gomez, who once again missed the target from a good position.
Argentina did not have to wait long before regaining their momentum in the second half and scored their third goal just two minutes into the restart.
Di Maria floated in a well-measured free-kick from the left flank that Federico Fernandez headed home from just yards out past substitute goalkeeper Roman Weidenfeller.
The United player himself scored Argentina’s fourth goal just three minutes later when he sprinted down the right flank and got the better of Weidenfeller with a beautiful chip.
The goals continued to come at the Esprit Arena, as Andre Schurrle pulled one back for the Germans on 52 minutes.
The Chelsea forward’s initial effort from a corner was saved by Romero, but the 23-year-old made no mistake from the rebound.
Argentina continued to create chances with Di Maria the heartbeat of their every move, but it was Germany who came closest to scoring the sixth goal of the match with 16 minutes remaining when Reus’s effort came back off the post.
The 2014 World Cup winners did make it 4-2 just a couple of minutes later thanks to an effort from Mario Gotze that was deflected into his own goal by Fernandez, but the evening belonged to Di Maria and Argentina.