The Wallabies were led by a stunning performance by Reece Hodge, who scored two tries and played a part in two others to put his stamp on the game.
Australia scored five tries to Argentina’s two - but some subpar goal kicking from Bernard Foley allowed the Pumas to stay in the contest, before the Wallabies pulled away late.
Another star for the green and gold was flanker Jack Dempsey, who worked in tandem with the rest of the Wallabies forwards to combat the aggressive Puma pack.
Australia hit the scoreboard first through the boot of Foley in the 15th minute - and that lead quickly grew five minutes later when Marika Koroibete rumbled down the left wing to score his third try in his second start.
The Pumas hit back shortly after when Matias Alemanno scored under the sticks in the 25th minute after some relentless pressure on their first entry into the Wallaby 22.
Nicolas Sanchez then gave the home side their first lead of the game in the 30th minute when he slotted a penalty goal to put his team ahead 10-8.
The Wallabies re-took the lead in the 34th minute when Will Genia found Hodge in a yawning gap on the right wing to stroll over the line untouched to give Australia a three-point lead when Foley missed his second conversion of the game.
A penalty goal to Nicolas Sanchez in the 38th minute levelled the scores heading into the major break - and giving plenty of hope to the home crowd in Mendoza.
In the second half, the flood gates opened for Australia - as Michael Hooper opted to attack the Pumas defence instead of taking the easy three points, and it paid off in the 52nd minute when Bernard Foley stepped through the line to score a five-pointer and re-take the lead.
Argentina struck back minutes later through Santiago Gonzalez Iglesias - but had no answer for Reece Hodge, who found shortly after and set up an open-field try for Will Genia in the 61st minute, setting the score at 27-20.
Foley shook off his kicking rust by nailing the conversion - then added an extra penalty goal with 10 minutes remaining to widen the gap to 10 points, when Matias Kremer was shown a yellow card.
Hodge sealed the game in the 77th minute on the back of some smooth ball movement down the right touchline - and a conversion to Foley locked the final score at 37-20.