Germany flew into a 2-0 lead thanks to first-half goals by Serge Gnabry and Kai Havertz, but Lucas Alario turned the game in the second-half when he came on for Argentina.
The Leverkusen striker pulled a goal back, then set up Lucas Ocampos for the late equaliser against a German team which included four debutants.
Freiburg pair, defender Robin Koch, a late call-up on Monday who was thrust into a makeshift back three at the last-minute, and striker Luca Waldschmidt started.
Leverkusen forward Nadiem Amiri and Schalke midfielder Suat Serdar came on to make their second-half debuts.
The Germans had already been forced into a hastily re-arranged defence as Koch replaced centre-back Niklas Stark, who pulled out before kick-off with a stomach bug.
Despite 13 withdrawals due to either illness or injury, Germany impressed early against an Argentina team missing Messi, Sergio Aguero and Angel di Maria.
With Messi suspended for comments made at the Copa America, Juventus' Paulo Dybala partnered Lautaro Martinez up front for Argentina.
This match was a repeat of the 2014 World Cup final, yet Argentina's Manchester United defender Marcos Rojo was the only survivor when the Germans won in Rio de Janeiro.
He partnered Manchester City veteran Nicolas Otamendi in an Argentina defence which crumbled early on.
A week after scoring four goals for Bayern Munich at Tottenham, Gnabry put Germany ahead on 15 minutes.
The winger used his pace when Atletico Madrid's Angel Correa lost possession to get in behind the defence to stab the ball past Argentina goalkeeper Augustin Marchesin.
When Rojo then lost the ball to Waldschmidt, Gnabry turned provider, using his pace to present Havertz with a simple tap-in on 22 minutes.
Argentina let their frustrations show as Otamendi and Rodrigo de Paul were booked for clattering Julian Brandt and Gnabry respectively.
It should have been 3-0 when Brandt just failed to connect with a Niklas Suele header with the goal at his mercy as it stayed 2-0 at the break.
However, the South Americans had the best of the second-half, starting when Argentina coach Lionel Scaloni put Alario on for Dybala on 62 minutes.
The Leverkusen striker showed his strength in the air to head past Barcelona goalkeeper Marc-Andre ter Stegen four minutes later.
The visitors equalised when Alario set up Sevilla's Lucas Ocampos, a second-half replacement for Correa, to blast past ter Stegen five minutes from time.
The match was preceded by a minute's silence in memory of the two people shot dead in the German city of Halle earlier Wednesday in an anti-Semitic attack.