Die Mannschaft showed plenty of positive signs throughout the contest, but were never able to recover after keeper Ron-Robert Zieler's first-half dismissal
The Hannover keeper was given his marching orders after half an hour for bringing down Jose Sosa in the area, though Lionel Messi saw his resulting penalty saved by substitute keeper Marc-Andre ter Stegen.
However, Sami Khedira's own goal on the stroke of half-time gave Argentina a lead they would never relinquish, with Messi atoning for his spot-kick faliure with the visitors' second goal on 52 minutes.
Angel Di Maria's stunning drive, from 30 yards out, sealed the victory with just over a quarter of an hour to go, rendering Benedikt Howedes' 81st minute header nothing but mere consolation.
Things looked to be so different for Germany after a positive opening, where Marco Reus fired the first warning shot in the 2nd minute, with a drag across the face of goal after a mazy run past a few defenders.
Miroslav Klose’s enterprising foray down the left flank fashioned the next opening for Die Mannschaft after 12 minutes, but Mesut Ozil was unable to make the most of his cutback, with Sergio Romero able to block.
Argentina played some entertaining football of their own and were able to cause problems in the attacking third. Their movement and interplay out wide was particular cause for concern, though Messi struggled to cope with the attentions of the home side's defence.
However, Germany looked to have a slight edge and continued to create better chances, with Thomas Muller's goal-bound effort blocked by his own team-mate Ozil from close range.
But the complexion of the match would change forever on the half -hour mark, after Sosa was brought down by Zieler in the box after a quick dart past the German backline.
The 23-year-old was sent off, with Ter Stegen coming off the bench to replace Thomas Muller and faced with the task of denying Messi from the penalty spot.
But with Messi's penalty a weak one, the 20-year-old keeper was quick to who get down well to smother at his left post.
Germany were boosted by the save, and came within inches of taking the lead two minutes before half-time, when Reus released Marcel Schmelzer on the overlap, whose low centre was just missed by the toe of Klose.
But it would be Argentina who would strike just before the break, after a wild attempted clearance from a corner by Khedira instead resulted in him deflecting the ball into his own net.
The home side thought that they had equalised, five minutes after the restart, when Reus hit the woodwork with Khedira working the rebound in for Ozil to turn home.
However, an offside call halted the celebrations of the Commerzbank Arena crowd and they were further silenced two minutes later when Argentina doubled their lead.
Messi had not been at his best all game, but would took full advantage of Germany's numerical deficit, slotting home unmarked after he was teed up by Gonzalo Higuain at the end of a flowing counter-attack.
The Barcelona star nearly made it 3-0 shortly after an hour with a trademark dink over Ter Stegen, but his finish bounced the wrong side of the post.
Time was slowly running out for 10-man Germany to find a way back into the game. Substitute Andre Schurrle attempted to reduce the arrears with a stinging drive from distance, but Romero was able to save his effort.
But there would be no way back for Low's men after the 73rd minute, when Di Maria took aim from 30 yards out and buried an unstoppable effort past the helpless Ter Stegen.
Howedes pulled a goal back on 81 minutes after nodding in a cutback from Mario Gotze, who had done well to exploit a pocket of space behind the Argentine defence.
Germany finished with a late flourish in the opposition half, but the South Americans nearly scored a fourth late on after Higuain fired Messi's through ball onto the post.