The rocket, carrying technology akin to a "small Hubble" telescope, lifted off - blasting nearly 350 kilometers (218 miles) into the night sky - in the first of three scheduled launches from the Arnhem Space Centre.
"It's a historic time for us as a company, but it's also historic for Australia," Equatorial Launch Australia CEO Michael Jones told AFP ahead of the launch.
Jones, whose business owns and runs the launch site in Australia's far north, called it a "coming out" celebration for the country's space sector, and said the opportunity to cooperate with NASA was a watershed moment for the country's commercial space enterprises.
Following a series of weather and wind delays, the suborbital sounding rocket launched into space to explore x-rays emitted by the Alpha Centauri A and B systems.
The rocket's cargo was to collect data on the star systems after reaching apogee before parachuting down to Earth.
According to NASA, the launch provides a unique view of distant systems and opens up new opportunities for scientists.
"We're pleased to be able to launch critical research missions from the Southern Hemisphere and study objects that we can't see from the United States," said Nicky Fox, head of NASA's Heliophysics Division in Washington, when the project was announced.
Jones said the unique location made preparations difficult, with years of effort to obtain regulatory permission and the requirement to transport rockets on barges to the launch site, which is approximately a 28-hour drive from Darwin in northern Australia.
"I believe it'll be a tremendous relief for the team that it's done," he remarked.
But, with the next launch scheduled for July 4, the respite would be brief.
"We need to dust ourselves off, take a day off, and then get back into it in preparation for the next launch, which is just as essential."
It is the first NASA rocket to launch from Australia since 1995, and Prime Minister Anthony Albanese welcomed the initiative as the start of a "new era" for the country's space sector.