They never looked back from there with Folau, halfback Will Genia, his replacement Nick Phipps and rookie hooker Jordan Uelese sharing the five- pointers.
After exchanging early penalty kicks, the Pumas took the lead in the 23rd minute halfback when Martin Landajo spun out of the ruck to dive over.
Folau's first came after the Wallabies moved the ball quickly from one side of the field to another before Bernard Foley found his man on the fly.
Foley had a big game, kicking at 100 per cent to contribute 15 points and also pulled off a try-saving tackle in the second half.
Argentina five-eighth Nicolas Sanchez broke the 10-10 deadlock with a penalty kick four minutes before halftime - with the Pumas looking to crack their first win on Australian soil since 1983.
The Wallabies lifted their intensity and once they got their noses in front through Kepu and then Folau's second try they took full control of the game.
Genia's try came after some sustained pressure on the Pumas scrum which saw Enrique Pieretto yellow-carded for collapsing the scrum after multiple penalties.
Australia travel to South Africa to take on the Springboks in Bloemfontein in their next encounter in a fortnight.