Argentina led with an eighth-minute penalty, but Folau beat four opponents to cross over, while Christian Leali'ifano added three penalties.
McKenzie gambled during the week when he dropped star halfback Will Genia to the bench, but the move paid dividends. Genia's replacement Nic White performed well throughout the match and White's kicks for touch in the first half were impressive enough that the ACT Brumbies No.9 played out the entire match.
Australia captain Ben Mowen, standing in for the injured James Horwill, said the win was rewarding despite the close scoreline.
"I thought the early results we got, a couple of early penalties, that was a big statement from where we were last week," Mowen said, referring to the Wallabies' poor scrum performance in a 38-12 loss to South Africa.
"We had to play disciplined in terms of field position near the end, and had to manage the territory. We did that."
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Scores:
Australia 14 (Israel Folau try; Christian Leali'ifano 3 penalties), Argentina 13 (Juan Manuel Leguizamon try; Nicolas Sanchez conversion, 2 penalties). HT: 14-3.
- AP