Messi marked his 1,000th professional game with his 789th goal - his first in a knockout match at the World Cup - and almost everything good that Argentina created going forward went through the little number 10.
It was always going to be a tough game against a Socceroos team who muscled their way into the knockout stages with a brand of football that relied on each player covering huge swathes of turf and tackling anything that moved.
The Australians, who have just refused to accept they are beaten during their Qatar campaign, got back into the contest with a late deflected Craig Goodwin (30) strike and had two good chances to equalise in the last few minutes.
Argentina's teak tough defenders matched the physicality of the Australians all evening, however, and they will take due credit for blocking Aziz Behich's shot after the full back's mazy late run through the box.
Emiliano Martinez (30) also had a good night and capped his fine display in the Argentina goal by stopping Garang Kuol's goalbound shot from close range with a save in the final seconds.
Further forward, though, Argentina will surely need to produce more penetration from the midfield and wide players in contests to come, starting with their quarter-final against the Netherlands next Friday.
Australia's compactness in the middle of the park forced the Argentinians to look wide in search of space but there was no Angel Di Maria (34) to share the attacking load with Messi because of the winger's calf injury.
Argentina slowed the game down as they do, but the rapier strikes that are supposed to follow the variation in pace rarely materialised unless Messi was receiving the ball, which he almost always did with his back to the goal.
In the 35th minute, however, Messi received a glimpse of the goal after a slick move from a free kick and made no mistake, firing a laser-guided shot through the legs of Australia's Harry Souttar (24) and into the far corner of the net.
"It's a privilege to play with Messi," said right back Nahuel Molina (24). "With him on the pitch we know that we just need to be patient because he is the ace up our sleeve."
Argentina's second goal came gift-wrapped when Julian Alvarez (22) pounced on a mistake by Australia goalkeeper Mat Ryan (30) and, apart from one Lautaro Martinez (25) effort blasted well over the bar, there were precious few other chances.
Messi, however, has long become accustomed to carrying a huge load for his country and three goals in four games in Qatar shows he might be approaching the kind of dazzling form that might take Argentina deep into the tournament.
The target is to finally add the World Cup to his already glittering collection of trophies and it would take a brave man to bet against him doing it.
