Fullback Michael Harris kicked 20 points, including five first-half penalties to put Australia 15-9 ahead at halftime as the Wallabies made the fewer handling mistakes with a slippery ball in damp conditions.
Australia’s third victory in the elite southern hemisphere tournament saw them finish equal with South Africa on points, but secured the runner-up position by virtue of having won more games than the Springboks.
The world champion All Blacks crushed South Africa earlier on Saturday for a clean sweep of six wins, while Argentina had to settle for bottom place, but enjoyed an encouraging debut with a draw and five mostly competitive defeats.
“The [Argentina] team really gave their all. There were some mistakes, especially in the first half, which finally cost us the match,” Pumas winger Gonzalo Camacho said.
“We gave away a lot of penalties, which was something we had set out to avoid, and the Australians got most of their points that way,” he told reporters.
Pumas prop Rodrigo Roncero, a veteran of three World Cups, came off to a standing ovation four minutes from the end in a fitting farewell in his 55th and last Test.
“He’s a master, there are no words to describe him,” Camacho said.