Australia finished the southern hemisphere's elite championship second behind winners New Zealand, with South Africa third and the Pumas ending their debut season in the tournament with a draw and five defeats.
Australia struck their telling blow with Ioane's try with 15 minutes remaining, right after surviving Argentina's most dangerous onslaught that almost delivered the Pumas a try.
From a scrum on Argentina's 22-metre line, the ball came out to Ioane who was in the centre and the wing cut through a gap in the defence to touch down under the posts with Harris converting.
Replacement wing Juan Imhoff scored a late try for the Pumas which was converted by centre Marcelo Bosch. Flyhalf Juan Martin Hernandez slotted over three penalties and Bosch one.
Harris's steady kicking from penalties gave the Wallabies a 15-9 halftime lead.
He put three over early as Australia went 9-3 up and converted his fourth from under the posts in the 23rd minute after an infringement by Argentina when Australia threatened to score a try.
Argentina lost lock Patricio Albacete to the sin bin two minutes later but the only advantage Australia were able to take was Harris's fifth penalty. Hernandez then failed with two attempted penalties in the dying minutes of the half.
Australia's replacement back Brett Sheehan was sin binned with less than six minutes remaining.
