It left the 14,281 Gold Coast fans - the lowest home test attendance this century - breathing a huge collective sigh of relief.
Skipper Michael Hooper scored a double but it was halfback Nick Phipps who shone as bright as any player, setting up what seemed to be the match-sealing try to winger Peter Betham for a 29-13 lead with 20 minutes left.
But the Pumas stormed back, punishing Wallabies' mistakes with tries to outside backs Marcelo Bosch and Joaquin Truculet for a 29-25 scoreline and tense finish.
Man-of-the-match Bernard Foley made it a seven-point gap when he kicked his fifth penalty goal with five minutes to go on a slippery night.
For the third straight home test, the rain came down as the game kicked off but it didn't deter Australia, looking to rediscover their attacking mojo, from playing a fast, ball-in-hand game.
And they did it brilliantly to start with, producing an opening six minutes of exquisite rugby.
Hooper scored after 10 straight phases that rolled the ball forward 60m from the opening lineout of the game, finished when the skipper burst on to a perfect cut-out pass from Foley.
But, when they made their first error, failing to secure the ball from a Sekope Kepu charge, the Pumas "Panther" - Manuel Montero - pounced.
The lanky winger, who is a target of the Western Force, showed his class with a 55m sprint down the sideline, leaving Betham, Hooper and Foley in his wake.
From there, Australia, not helped by the slippery conditions, lost their precision and some of their nous.
Argentina's line speed pressured them into errors but the Wallabies were also their own worst enemy - shown by Foley butchering a certain try by ignoring Rob Horne 5m from the line.
The home pack dominated the lineout and held their own in the scrum for 78 per cent of first half possession but had to be satisfied with just three Foley penalty goals for a 14-7 lead at the break.
Hooper extended the lead with an opportunistic try just after halftime, and at that stage it looked like his side was in for an easy night.
Wallabies coach Ewen McKenzie confirmed Polota-Nau was unlikely to make next week's trip to South Africa and would have scans on his ankle sprain.
Betham is also set to miss the final two Rugby Championship tests after the foot injury that sidelined him for much of the Super Rugby season flared up again.
"That hooker and winger curse continues to trouble us, so we need to go and look for new guys again," McKenzie said.
Argentina coach Daniel Hourcade rated the Pumas' performance their worst of the tournament, despite being proud of their comeback.
"I think we have to play with the ball, having a good scrum is part of our DNA, but today Australia was really superior, they were better than us with the ball," he said.
The Pumas also suffered worrying injuries with centre Juan Martin Hernandez (knee) and flanker Juan Manuel Leguizamon (calf) replaced in the second half.
Wallabies 32
Pumas 25
- AAP
