The Wallabies conceded two tries in the first four minutes and were 31-7 down at half time but after coach Michael Cheika launched a blistering team talk they came out and dominated the second period to hammer a hapless home side.
Izack Rodda, Israel Folau and Dane Haylett-Petty scored tries within 10 minutes of the restart before David Pocock crossed and Haylett-Petty grabbed his second with 15 minutes remaining to make the score 42-34.
Bernard Foley scored a penalty six minutes from time to add to his six conversions and although Tolu Latu got a yellow card for a reckless elbow with four minutes remaining the Pumas could not make their advantage count.
Argentina, who needed a win or a draw to condemn the visitors to last place in the championship, looked shell shocked and could manage only a penalty after the break.
It was the biggest comeback in Rugby Championship history and the largest amongst Tier One nations. Chile held a 27-0 lead at halftime before losing 35-34 to Uruguay in 2007.
The result means the Wallabies leapfrog Argentina to finish third in the final table, behind South Africa and winners New Zealand.