The hosts were down 20-3 before clicking into top gear with 10 minutes to play in the first half on Sunday morning (AEST), scoring four tries in the last nine minutes.
It's the most points the Wallabies have conceded in a Test, beating the 61-22 hammering they copped in South Africa in 1997.
The flogging followed a gritty 20-19, last-gasp win over Argentina in driving rain seven days ago.
This time, in brilliant sunshine, Australia looked on song again when Ben Donaldson found joy down the blindside to set up fullback Andrew Kellaway for their second try and create a 17-point buffer.
Back-rower Carlo Tizzano had earlier barged over for the game's first try after a Los Pumas' penalty goal.
But the hosts flicked the switch 10 minutes before the break, Mateo Carreras finishing some superb work from Pablo Matera before skipper Julian Montoya breached the ragged Wallabies defence.
Joaquin Oviedo evades Wallabies defenders to go over for a try in Santa Fe. (AP PHOTO)
They came close to scoring again before the break but didn't relent at the resumption, an early unforced error from Marika Koroibete gifting field position that led to Juan Martin Gonzalez scoring.
Pablo Matera's try came after Schmidt had replaced his halves, who could only watch as Argentina hit top gear and Joaquin Oviedo's try made it 38 consecutive points.
Koroibete was pushed into touch after halfback Tate McDermott put him through a gap, the replacement half doing it himself, tapping and darting through traffic to stop the rot.
There was still a glimmer of hope with 10 minutes to play, Argentina emphatically shutting the door in a devastating final passage that created some unwanted history for Schmidt's men.
Juan Cruz Mallia strolled over twice in mere minutes and Oviedo added another to complete the carnage. Australia's next assignment is New Zealand in Sydney on September 21.
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