The Wallabies' scrum dominated the Pumas' and player of the match Will Genia, Kurtley Beale and comeback king Christian Leali'ifano put on an assured kicking display not seen for a long time from an Australian Test team.
Most pleasing was Australia's defence, keeping the Pumas try-less until the 74th minute with disciplined, patient defence in front of an appreciative 31,559 crowd at the iconic Brisbane ground.
"Really pleasing, we love coming up here ... really pleased with our play and how we bounced back from a short week's turnaround," captain Michael Hooper said.
It was the victory the team and its fans needed to keep faith with coach Michael Cheika's plan as time ticks down to the start of Australia's World Cup campaign.
Two tough Tests against New Zealand are bearing down but the Wallabies have a week off to consolidate and map out a plan for their imperious old foes, who look to have lost key forward Brodie Retallick to a shoulder injury.
The Wallabies faltered when Cheika made mass changes in the second half but held on with steely defence and a ferocious work rate from standouts Hooper, Marika Koroibete, Isi Naisarani and the rest of the pack.
Genia and Leali'ifano were given heroes' send-offs, the Brisbane crowd appreciative of Genia's long career in Queensland and Leali'ifano's extraordinary personal comeback after a battle with leukaemia.
Hooper directed his No.10 to take the shot at goal that put Australia on the board 3-0 in the 11th minute, reassuring Australian fans who watched him make the opposite call when the Wallabies trailed 14-10 just before halftime in South Africa last week.
The next 10 minute period was high-paced ping pong stuff, both teams intent on keeping the ball in play.
At times Australia's hunger for pace didn't match their ball-handling skills. At one stage the Wallabies fought hard to shut down a try and turn over possession only for a hasty offload from Lukhan Salakaia-Loto to undo their good work.
The Aussie scrum held up well in the heat of that moment, earning a penalty on their own 22m line.
Sekope Kepu was similarly wasteful with the next turnover, giving the Pumas their chance to get on the board. Five-eighth Nicolas Sanchez kicked it from right in front to level the scores at 3-3.
Australia continued to get themselves out of danger and turned their scrum into a weapon, launching a devastating attacking raid off the 10m line and using a midfield decoy runner to unleash Koroibete with the ball. The Fijian winger passed to Beale who got it away to Reece Hodge, the towering winger slicing back inside to score.
Leali'ifano did well to convert at put the Wallabies out to a 10-3 lead, which they took into the break.
Taniela Tupou replaced Kepu at halftime and James Slipper came on in the 47th mintue for Allan Ala'alatoa.
The Aussie scrum went to a new level, earning a penalty in front of the posts that Leali'ifano converted to put Australia out to a 13-3 lead, before walking off to appreciative applause from the Suncorp crowd.
Matt Toomua replaced his old Brumbies teammate, and Genia was replaced by Nic White minutes later. The crowd gave the local kid a huge send-off, not lost on Genia, who played his last Test match at his home ground. He will play in Japan with former Reds partner Quade Cooper.
The Wallabies attack faltered under the new combinations – Luke Jones replaced No.8 Naisarani - but their defence held up under repeated Pumas raids in Australia's half and the Aussie scrum continued to dominate.
James O'Connor was injected with 11 minutes to go, slotting in at inside centre after Tevita Kuridrani left the field and Kerevi slid across to 13.
A Luke Jones offside blunder handed Argentina an attacking opportunity they did not waste. No.8 Facundo Isa scored off an 11-man lineout and reserve playmaker Joaquin Diaz Bonilla converted to put the Pumas within a converted try of victory with just five minutes left on the clock.
Toomua missed a penalty goal with three minutes to go, but Australia wanted the win and worked hard to pressure the Pumas inside their 22, a valedictory scrum penalty the icing on top of a much-needed win.