Die Mannschaft showed plenty of positive signs throughout the contest, but was 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 halftime would give Argentina a lead it 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 second 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 its own and was able to cause problems in the attacking third. Its movement and interplay out wide was a particular cause for concern, though Messi struggled to cope with the attentions of the home side's defense.
The complexion of the match would change completely on the half hour mark, after Sosa was brought down by Zieler in the box after a quick dart past the German backline.
The Hannover keeper was sent off, with Ter Stegen coming off the bench to replace Thomas Muller, and face Messi from 12 yards out. However, the match would remain goalless, as Messi's weak penalty was read by the 20-year-old keeper, who got down well to smother at his left post.
Argentina 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.
Germany thought that it had equalized 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 on Khedira halted celebrations of the Commerzbank Arena crowd in their tracks, and they were further silenced two minutes later when Argentina doubled the lead.
Messi had not been at his best all game, but would take full advantage of Germany's numerical deficit, slotting home unmarked after he was teed up by Gonzalo Higuain from a flowing counterattack.
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.There would be no way back for Low's men after the 73rd minute, after Di Maria took aim from 30 yards out and buried an unstoppable effort past the helpless Ter Stegen.
Howedes would pull one 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 defense.
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.