Fly-half Santiago Carreras kicked 23 points for the visitors as Argentina nearly let a win slip from their grasp against an Australia side that lacked patience and polish at Sydney's Allianz Stadium.
After falling to a last-gasp defeat to Australia in Townsville last week, Argentina must have been fearing a repeat on Saturday when, inspired by substitute No.10 James O'Connor, the Wallabies laid on 19 points in the final 13 minutes.
But Australia couldn't land the knockout blow and now enter the final two rounds of the Rugby Championship with two Tests against New Zealand with a 2-2 record.
A late comeback would have papered over the cracks given how poorly Joe Schmidt's side played at times on Saturday.
The Wallabies gave away 15 penalties to Argentina's eight and it was only with O'Connor at the helm - and when Carreras was sinbinned in the 66th minute - did the home side show their quality.
Carreras had got Argentina on the board inside two minutes with a penalty goal before a lovely bit of inter-play between fullback Andrew Kellaway and Joseph-Aukuso Suaalii saw Australia hit straight back.
Suaalii steamrolled his way through the Argentine defence to crash over, with fly-half Tane Edmed converting the fourth-minute try from out wide.
Edmed had some nice moments, including a quick-thinking 50-22 on his first Test start, but was all at fault for Argentina's first try which came soon after Suaalii's impressive opener.
The playmaker's clearance from a free kick was charged down by Argentina captain Julian Montoya, who scooped up the loose ball and touched down to put his side in front.
Australia did well to survive a period when they were down to 14 men after winger Max Jorgensen was sinbinned for a knockdown in the 18th minute.
But Carreras, who had converted Montoya's try, kicked three further first-half penalties to give Argentina a 19-7 halftime lead.
If it weren't for a few ill-considered plays that left head coach Felipe Contepomi screaming into his radio, the Pumas could have easily led by more than just 12 points.
But the Wallabies failed to heed their lessons of the first half and watched on as Carreras guided two further penalties through the posts.
Needing a change of pace with his side down 25-7 after 55 minutes, Schmidt brought Edmed off for O'Connor.
It took Carreras adding his seventh penalty of the afternoon soon before he was sent to the sinbin for Australia to spark into life.
In a two-minute onslaught the Wallabies hit Argentina with two tries.
O'Connor was the conductor as he combined with Suaalii to send Kellaway over under the posts.
Then O'Connor spotted a gap on the blindside and sent Filipo Daugunu down the left wing to make it 28-19 and set up a grandstand finish.
Daugunu added another try with a minute left to make it a one-score game, but Australia couldn't get out of their own half as Argentina ground their way to a win.
