Cheika said he was surprised by South Africa's 57-0 loss to New Zealand in Saturday's other Rugby Championship test and warned of a backlash from the Springboks when the Wallabies play them in their next match in Bloemfontein on September 30.
Coach Michael Cheika demanded more urgency and pace from his team in the second half and the Wallabies responded to dominate the Pumas.
Australia was also ruthless in taking advantage of the sin-binning of Pumas prop Enrique Pieretto, running in three tries in the final 10 minutes to halfbacks Will Genia and Nick Phipps then second-Test hooker Jordan Uelese, the first of what should be many.
"At halftime I didn't have to say anything", Cheika told Fox Sports' Rod Kafer after the match.
But he felt a lift in their intensity and urgency in the second half was key to the Wallabies revival, with the victory coming after last week's disappointing draw with South Africa.
It followed a heartbreaking 35-29 defeat to the All Blacks in Dunedin last month when the Australians relinquished a 17-point lead as New Zealand snatched the winning try with two minutes left.
The home side hit back just five minutes later as the ball was sent out to the right to Folau, who went over with Foley tying things up with the conversion.
The Wallabies paid for their indiscipline in their own half with Sanchez putting the Pumas ahead 13-10 with a penalty goal nearing half-time.
Front-rower Kepu scored off a pick-and-drive close to the Pumas try-line and Folau completed his double with his 30th Test try off a long cut-out Will Genia pass.
Australia overcame a awful first-half performance to register their first win of the Rugby Championship as Argentina once again hit the wall and conceded late points in Canberra to ruin their early success.