The Wallabies have a runners-up spot behind champion New Zealand in their sights with one match against the Pumas to play after scoring three tries in their first ever Test in Townsville, moving above South Africa after it was beaten by the All Blacks.
Emiliano Boffelli dragged a penalty wide before Reece Hodge burst through a tackle after throwing a dummy and applied the finish after a swift side-step.
Hodge's early opening try came after a powerful run from the outstanding Samu Kerevi, who crashed over for a score of his own and Quade Cooper made it three successful kicks out of three to put the vibrant Wallabies 17-3 up at half-time after a penalty from Boffelli.
Julian Montoya touched down early in the second half at the back of a driving maul, but Boffelli missed the conversion and was also off target with another penalty.
James O'Connor sent a kick sailing through the posts after coming on for his first Test of the year while Marcos Kremer was in the sin-bin.
Replacement five-eighth half O'Connor set up Kellaway, the leading try scorer in the tournament, for a simple finish nine minutes from time in another impressive showing from Dave Rennie's men.