Argentina down ten-man Germany
Messi made it two in the 52nd minute and Angel di Maria added a third in the 73rd minute before Benedikt Howedes grabbed a late consolation for the hosts.
Zieler had only been involved in the game once before he was off the field again after only his second intervention. This one was against the rules as he pulled Jose Ernesto Sosa down to give away a penalty and see a red card on only his second appearance for the national team, the first being an equally-forgettable occasion when he conceded three in a draw with Ukraine.
Marc-Andre ter Stegen, whose Germany debut was equally forgettable, being the 5-3 defeat by Switzerland prior to UEFA EURO 2012, redeemed himself by denying Messi from the spot.
There was almost a similar incident at the other end when Mesut Ozil was sent through, but Sergio Romero was quick to pounce on the ball as the Real Madrid midfielder skipped past him.
Messi was again denied by Ter Stegen in the 39th minute when he let the ball get a bit too far in front of him, while Miroslav Klose was only inches away from turning Marcel Schmelzer's cross in as the game opened up with Germany reduced to ten men and Argentina becoming more adventurous.
The opening goal was in the air and it arrived on the stroke of half-time, with the Real Madrid pairing of Di Maria and Khedira combining, with the former sending in a corner which the latter deflected into his own goal at the near post.
Messi, Di Maria make sure
Germany almost levelled in the 50th minute when Marco Reus' 25-yard shot struck the post. The ball fell to Khedira, but he was in an offside position as he squared the ball for Klose to score a goal which was correctly ruled out.
Messi left Ter Stegen no chance with his next effort in the 52nd minute, a well-placed left-footed shot from just inside the penalty area which nestled in the bottom left-hand corner of the goal.
Messi missed the chance to wrap up victory in the 65th minute when he capitalised on a slip by Jerome Boateng and lifted his shot over the onrushing Ter Stegen, but just wide of the far post.
But the game was effectively over in the 73rd minute when, moments before being substituted, Di Maria drilled in an unstoppable shot from fully 30 yards to earn gasps from much of a shocked, yet appreciative crowd.
Messi rattled the post minutes later after dribbling his way past four Germany defenders, but there was a consolation for the hosts in the 81st minute when Borussia Dortmund midfielder Mario Gotze lifted the ball back from the goalline to his team-mate Howedes, who headed powerfully into the opposite corner.