With Argentina having held South Africa in Mendoza in August, there was never any doubt the Wallabies faced a tough task, and with injuries piling up and rumblings of discontent in the camp the preparation was far from ideal.
But coach Robbie Deans saw his team dig deep, their one try coming from Digby Ioane in the 65th minute, converted by Harris who missed just one kick all night.
Argentina came back at their visitors and guaranteed a tense finish when Juan Jose Imhoff was driven over the line, but Australia clung on.
For Argentina, Juan Martin Hernandez kicked three penalties in the first half to five from Harris.
Hernandez had to come off injured five minutes into the second half and Marcelo Bosch stepped up to kicking duties, slotting a penalty and adding the extras to Imhoff's try.
That try came four minutes after veteran prop Rodrigo Roncero bowed out of international rugby, substituted in the 73rd minute in his final Test.
Roncero has been a cornerstone of Argentinian rugby for 14 years and has appeared in three Rugby World Cups, helping the Pumas to their third-place finish in 2007.
The 35-year-old knew that signing off with a win against the Wallabies on his 55th appearance would have been the crowning glory of his career, but he was unable to play a part in the closing stages.
Australia's success earned them a second-placed finish, behind world champions New Zealand who won all six of their matches, in the inaugural Rugby Championship. Argentina finished bottom, with five losses and their one draw against the Springboks.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.