Playing in the mountain town of San Salvador de Jujuy, the Australians scored four tries to two to earn a gritty 27-21 victory in the first of two Tests in Argentina.
After opening his Test coaching tenure with successive victories over Japan, the clash with the world No.7 Pumas at altitude was the first big trial for Kiss's men.
With two late tries denied, Kiss said the performance was far from perfect but there was still plenty to like, including their composure in front of a hostile home crowd.
"There's still a few little clunky bits in our game," the coach told Stan Sport.
"Speaking to Allan (Alaalatoa) and Fraser (McReight), the boys were calm out there for the whole game, they didn't lose the run of themselves in any way when it wasn't going quite right and they kept going back to the things that worked for them.
"Even that second half, we get one of those tries, perhaps we can put the foot on the accelerator even further, but I thought a good, industrious effort by the boys."
Despite ideal conditions, both sides made plenty of errors in attack with the Wallabies forward pack proving the difference, with three turnovers at lineout including a 79th minute steal by Charlie Cale.
With skipper Harry Wilson among the players rested, his replacement at No.8, Rob Valetini put the visitors on the front foot with a game-high 19 carries.
Barn-storming lock Josh Canham produced four off-loads while flanker Fraser McReight was named man of the match with some crucial turnovers at the death.
Winger Max Jorgensen credited the forward pack for their efforts.
"The piggies are doing an absolute job for us there up front," he told the broadcast.
"Those line-out steals take so much pressure off us as a backline and all those scrum penalties as well.
"They put in a huge shift here today, that's a big reason why we got the win."
The Wallabies led 12-0 early and were up 22-14 at halftime, with hooker Brandon Paenga-Amosa, Carter Gordon and McReight all crossing the line.
Tries by fullback Geronimo Prisciantelli and No.8 Joaquin Moro kept Argentina in the hunt while a valuable penalty strike by Ryan Lonergan after halftime secured the eight-point lead.
The halfback was an early casualty in the second half, seemingly hurt while making a try-saving tackle.
Kiss later cleared him of serious injury and said he always planned a short shift for Lonergan who had been ill with the flu.
The margin was then reduced to one point in the 52nd minute with Pumas prop Boris Wegner burrowing over.
However the visitors were able to kick away with an impressive team try three minutes later, with flanker Tom Hooper collecting the five-pointer.
It looked like they would have some breathing room in the final 10 minutes but a try by Jeremy Williams was denied upon review, and then Tate McDermott was held up over the line to set up a nerve-wracking finale.
The desperate Pumas did their best to find another try but errors, as well as scrambling defence, saw the Wallabies to secure an important win away from home.
With the Australians also claiming a victory over Italy in July in Joe Schmidt's last Test as coach, it's the first time since 2021 they've won four in a row.
They will face Argentina in the second Test in Mendoza next Saturday night (Sunday 0700 AEST).
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