Kellaway's three tries took his season tally to eight, while Folau Fainga'a and Samu Kerevi also crossed to help the Wallabies rack up four successive wins for the first time in the southern hemisphere competition.
Replacement prop Thomas Gallo scored two consolation tries for the Argentines in the final quarter, but the Pumas will return home after a long and arduous tour without a win from their six matches in the championship.
The bonus-point victory ensured the Wallabies would finish second in the championship behind New Zealand.
Australia skipper Michael Hooper was pleased with how his team had rebounded after three losses to the All Blacks.
"Really stoked, we had three tough games on the trot against the kiwis so to turn things around and ... get four wins is showing some really nice stuff for us," said the flanker, who was sin-binned in the last minute.
The opening 27 minutes of the contest were a cagey battle for field position and it was not until Pumas lock Tomas Lavanini was shown a yellow card for a lineout infringement that Australia were able to add to Quade Cooper's early penalty.
Fainga'a almost immediately darted across the line from close range from a five metre lineout, and the hooker played an integral role in the second try seven minutes later.
In a set move, Fainga'a swept around the back of the lineout and his pass released Rob Valetini for a charge up the middle with the big number eight finding Kellaway in support to finish the job.
Emiliano Boffelli converted a penalty after a period of sustained Argentina pressure to reduce the deficit to 15-3 at the break but Australia grabbed their third try soon after the restart.
From a good attacking position, Cooper cleverly pump faked to open up a gap in the defence before sending Kerevi through it with a deft pass.
In the 54th minute, Kellaway skipped through a handful of tacklers for his second try, and his third followed four minutes later after Australia had engineered an overlap.
The Argentina team was selected without six squad players who breached COVID-19 protocols by leaving Queensland to travel to New South Wales during the week and were excluded from the championship.
The Pumas never give up, however, and Gallo twice found a way across the try line from close range in the last 17 minutes to make the scoreline a bit more respectable.
"I'm very proud of the effort of the players after two months away from home," said Pumas captain Julian Montoya.
"We played the whole 80 minutes very tough, but it's not enough. It would be nice to play at home after two years."