After Serge Gnabry skilfully put the hosts in front, Bayer Leverkusen midfielder Kai Havertz swept home Die Mannschaft's second of a game in which Argentina offered very little until substitute Lucas Alario pulled one back in the 66th minute.
Lionel Messi missed the game while he served a suspension but Lionel Scaloni fielded a strong team including Paulo Dybala, Lautaro Martinez and Roberto Pereyra in attack.
Low took the opportunity to give debuts to Gian-Luca Waldschmidt on the wing and Robin Koch in defence and was rewarded with an hour of dominance before a late rally culminated in Ocampos poaching an equaliser that silenced the crowd in Dortmund.
Argentina were undone after 15 minutes when Lukas Klostermann got around Angel Correa and played a low cross towards Gnabry, who nipped in ahead of three Argentina defenders and poked the ball into the far corner of the net from six yards.
Another Klostermann break brought Germany's second goal, the RB Leipzig wing-back pouncing after Marcos Rojo yielded possession and surging forward to feed Gnabry, whose slide-rule pass into the box found Havertz unmarked for an easy finish.
Marcel Halstenberg crashed a stunning 30-yard free-kick onto the underside of the crossbar before Argentina's Rodrigo de Paul hammered a similarly spectacular effort onto the post at the other end but at the interval the hosts deservedly led 2-0.
Emre Can forced Agustin Marchesin into a save on the edge of his penalty area early in the second half before Scaloni sent on Alario for Dybala.
The Bayer Leverkusen striker had been on the pitch just three minutes when fellow substitute Marcos Acuna picked him out with a floated cross from the left and he arrowed a header into the far corner of Marc-Andre ter Stegen's net.
A Joshua Kimmich free-kick tested Marchesin in the closing stages but the Porto goalkeeper punched it clear before Alario's run sliced Germany open and Ocampos side-footed home via a deflection off Can, beating Ter Stegen at his near post to Low's dismay.
Goooooool de la Albiceleste— TUDN USA (@TUDNUSA) October 9, 2019
A 5 minutos de que acabe el juego, Ocampo empata el partido en su debut... ¡Qué día para el argentino!
Alemania 2 -2 Argentina
🔴EN VIVO https://t.co/DsXCKlHnfD pic.twitter.com/O8HaJFhTks
What does it mean? Low's men took their foot off the gas
Germany face stiff competition from Northern Ireland and Netherlands to qualify for Euro 2020 but looked confident and incisive enough to beat almost anyone for an hour in Dortmund.
That assured display gave way to a disappointing half-hour in which Germany's inexperience perhaps took its toll.
Brandt bossed it
The best Germany teams of the last decade have always featured an imposing presence in attacking midfield, and Julian Brandt's high-pressing performance offered shades of Thomas Muller in his prime.
Rojo no show
Rojo went into this game having played just 30 minutes of Premier League football for Manchester United this season and it showed; he was hauled off at half-time.
Germany face Estonia on Sunday in the battle of top versus bottom in Euro 2020 qualifying group C, while Argentina play another friendly against Ecuador in Spain.