Australia held off a late fightback from Argentina to secure a much-needed victory, with former Ulster fly-half Christian Lealiifano kicking 11 points in his first test appearance since recovering from leukaemia.
Winger Reece Hodge scored Australia's only try in the first half of a scrappy Rugby Championship contest in Brisbane but Pumas number eight Facundo Isa crashed over in the 74th minute to set up a tense finish.
The home defence held firm to secure the twice world champions only a fourth victory in their last 14 tests and give them a chance of winning the championship for the first time since 2015, the last World Cup year.
It was Australia's first win of the year after their 35-17 loss to South Africa in their Rugby Championship opener and a big confidence boost before back-to-back tests against world champions New Zealand.
"It was a really tough game," said Australia skipper Michael Hooper.
"Our trust and commitment in defence was really great. We're playing a little bit different in attack and I'm really pleased with how we grew there."
Argentina, who ran the All Blacks close on home soil last week, will be disappointed with a seventh straight test defeat as they look to build towards the World Cup in Japan.
"We lost too many balls in the contact," said Pumas captain Pablo Matera.
"We had many chances to score but we didn't and that's why we see this result. We are growing and getting stronger and we have a tough game against South Africa in a couple of weeks. Hopefully we can get the win there."
Wallabies fly-half Lealiifano, returning to test rugby for the first time since his battle with leukaemia, kicked 11 points off the tee to help the home side's cause.
With both sides coming off defeats, the opening half hour was a gritty encounter in which Australia dominated possession but Argentina's kicking game ensured they had the better of the battle for territory.
Lealiifano and his Argentine counterpart Nicolas Sanchez exchanged penalties but there was little free-flowing rugby to entertain the modest crowd at Lang Park.
Australia's scrum did have a distinct upper hand and it was a solid set piece that created the platform for the opening try in the 32nd minute.
In the only move of genuine quality in the game, Lealiifano flipped the ball to Marika Koroibete coming off his wing and his charge up the midfield created the space out wide for Hodge to touch down in the corner.
Lealiifano extended Australia's lead to 16-3 with two more penalties before he made way for Matt Toomua 11 minutes into the second half.
Both teams continued to struggle with their handling and the Pumas were unable to put together enough of their neat passing combinations to breach a Wallabies defence which looked much better organised than against the Springboks last week.
Their scrum might have been struggling but there was nothing wrong with the Argentine lineout and it was from a catch-and-drive that they finally got their try.
The referee was already playing advantage after Australia had collapsed the rolling maul but the Pumas did not need it with Isa forcing his way across the line from close range to cut the deficit to six points with as many minutes on the clock.