Argentina, who have been grouped with defending champions New Zealand at the World Cup in England, could muster only three penalties from flyhalf Nicolas Sanchez.
Australia go into the decider in Sydney in two weeks' time equal on nine points with New Zealand after the All Blacks’ 27-20 victory over South Africa in Johannesburg.
Australia drew first blood with wing Joe Tomane’s 17th-minute try and went in 8-6 ahead at half-time.
They ran in a second try through replacement lock Dean Mumm just before the hour before centre Tevita Kuridrani and wing Adam Ashley-Cooper ran in two more in the final three minutes for the bonus point.
Flyhalf Bernard Foley kicked 14 points.
“It was great to come here and get the win,” Australia captain Stephen Moore said. “Argentina have a very strong scrum but like last week it was the boys who came off the bench who made the difference.”
Australia came from behind to edge the Springboks 24-20 late in last weekend’s match in Brisbane.
The Wallabies, who had threatened to breach the Pumas defence during a six-minute onslaught to start the match, made the breakthrough when Argentina's Sanchez kicked ahead from inside his own half and the ball was fielded by Israel Folau.
The fullback launched a lightning counter-attack, passing left to Foley who sent Tomane over in the corner.
Foley, who had a mixed game as place kicker, missed the conversion but slotted a penalty later in the half.
Sanchez kept Argentina in touch with two penalties, the second coming on the stroke of halftime.
Twice Australia had penalty decisions reversed for fouls in the first half as indiscipline, which had let them down in their defeat in Mendoza last October, crept into their game.
The Pumas' 21-17 win over Australia last year stands as their only victory in the tournament.
Folau was lucky not to be yellow carded in the seventh minute for barging into Sanchez’s back as the flyhalf rose to catch an Australian crosskick.
Replacement back Quade Cooper was sent to the sin bin in the second half for a neck-high tackle but Argentina failed to take advantage of their extra man, showing a lot of good running with the ball but little real penetration.
(This story was refiled to fix the spelling to 'cooper' in the sixth and 17th paragraphs)
(Reporting by Rex Gowar; Editing by Peter Rutherford)
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