Fly-half Santiago Carreras was instrumental for Argentina, contributing 23 points from seven penalties and one conversion, alongside a try from captain Julian Montoya.
The Pumas established a significant 21-point lead, reaching 28-7 in the 64th minute, before a late surge from the Wallabies.
Australia mounted a strong comeback in the final quarter with tries from Filipo Daugunu (two) and Andrew Kellaway, narrowing the deficit to just two points by the 80th minute.
Despite Australia's late pressure, Argentina held firm, with the Wallabies' final attack ending in an errant pass and a penalty against Max Jorgensen, allowing the Pumas to clinch the win.