The Wallabies scored five tries after the break in Salta to clinch a win that had appeared very unlikely at half-time, completing the biggest comeback in Rugby Championship history.
With the win, Australia avoided finishing bottom of the table and back-to-back losses to the Pumas for the first time in history.
Dane Haylett-Petty scored twice and Bernard Foley booted 15 points for the Wallabies, who kept the pressure from further increasing on under-fire coach Michael Cheika.
FULLTIME: The Wallabies have pulled off the biggest come back in rugby Championships history. The Wallabies were outstanding in the 2nd half scoring 38 points to defeat the Pumas. #ARGvAUS https://t.co/OqOi8SOZv8 pic.twitter.com/ACgbpe0wnr
— TheRugbyChampionship (@SanzarTRC) October 7, 2018
But the Wallabies' win only came after making the worst possible start, conceding 31 points in the opening 40 minutes.
The Pumas crossed twice in the first four minutes, Pablo Matera's beautifully angled run allowing him to break the line and score the opener, before the Wallabies were punished for a turnover as Emiliano Boffelli went over.
A superb Will Genia pass allowed Michael Hooper to respond for the visitors, but that – with Foley's conversion – would be their only points of the first half.
Argentina broke the Wallabies' line at will – including Santiago Gonzalez Iglesias easing through an attempted Foley tackle for a 31st-minute try – as Argentina piled on 31 first-half points.
Cheika looked to rally his team at the break and he got an immediate response as the Wallabies scored three tries in the first 11 minutes of the second half.
Izack Rodda was rewarded for a charge-down, Israel Folau crossed and Haylett-Petty went over in the corner to bring the Wallabies back into the match.
As Foley continued to deliver with the boot, David Pocock and Haylett-Petty scored in the space of three minutes as Australia took a lead they would not relinquish, despite a late yellow card to Tolu Latu.
63 l Poey is OVER!!
— Qantas Wallabies (@qantaswallabies) October 7, 2018
Photo Getty Images. Caption: Australia's Michael Hooper