Wind and rain at Subiaco Oval meant the match was never going to be a classic but a try from Israel Folau and nine points from the boot of Christian Leali'ifano gave Ewen McKenzie his first victory as Wallabies coach.
After a series defeat to the British and Irish Lions, back-to-back losses to New Zealand and a humbling on home soil by South Africa last week, the Wallabies were delighted to get any sort of win.
"It felt like an 100-0 win," captain Ben Mowen said in a pitchside interview.
"We hung in there and it was very rewarding for the side. Extremely tough conditions tonight and we had to simplify things to adapt to those conditions."
The Pumas, still searching for their first victory in their second year in the championship, seemed more affected by the conditions than the home side in the first half.
They earned the expected supremacy in the scrum, though, and held Australia scoreless in second half but were unable to drive home their advantage after Juan Manuel Leguizamon's try brought them to within a point of the lead with 15 minutes to go.
"We always knew it was going to be very close but at this level we cannot have a half like the first half, we didn't focus in the right way," said Pumas captain Juan Martin Fernandez Lobbe.
"After we scored the try, we can see why Australia has been up there since rugby started. They were very clever and they just made us play away from their half."
Argentina kicked off a new era in their new deepest dark blue strip and took a seventh-minute lead after Nick Cummins was caught trying to play the ball from his own line.
Flyhalf Sanchez made the tackle and kicked the penalty when the Wallabies winger was penalised for not releasing but Leali'ifano slotted two penalties over the next 10 minutes to put the home side ahead at 6-3.
With the Australian forwards showing a lot more dynamism than they had in their insipid defeat by the Springboks last week, the Wallabies always looked more likely to score the first try and it duly arrived after 28 minutes.
Quick hands from Quade Cooper and James O'Connor got the ball out to Folau on the right wing and the former rugby league international cut inside through four tacklers to touch down for his fourth test try.
Leali'ifano missed the conversion but added his third penalty right on halftime to send the Wallabies into the break with a 14-3 advantage.
The Pumas had the wind to their backs after halftime and camped in Australia's half going through phase after phase of attack, kicking their penalties for the corners and forcing Australia into scrum after scrum.
They finally got reward for their efforts on the hour mark with Sanchez's second penalty and four minutes later experienced centre Felipe Contepomi breached the Australian defence and found big number eight Leguizamon in support.
Sanchez converted to leave the Wallabies with just a one- point lead but the Australian backs kicked the leather off the ball to keep the action in the Argentina half and, if anything, looked the more likely team to score.
Leali'ifano missed two penalty attempts into the swirling wind but the Wallabies held on to hand McKenzie his first taste of victory in four tests since he replaced Robbie Deans after the Lions series.
"It's good for confidence to get a win," McKenzie told Fox TV. "We made hard work of it at times in the second half but it was difficult conditions.
"Not extravagant, but given the conditions you've got to find a way and I think we did that."