They led only 14-10 at the break, before raising their game and scoring five unanswered second-half tries against their error-prone opponents.
The result was a far cry from the 74-6 thrashing New Zealand inflicted on the American Eagles at the same venue last year.
Nonetheless, Australian prop James Slipper expressed satisfaction with the result after his first game as captain.
"It was a good win," he told NBC Sports Network in an on-field interview. "We came here to win. We ended up doing that."
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Slipper diplomatically praised the Americans and predicted they would more than make up the numbers at the World Cup in England.
"Proves how good the Eagles are," he said. "They came out in that first half and played some really great rugby. They're going to go far in the World Cup. Credit to them. Both teams showed physicality."
American captain Chris Wyles lamented that his team could not replicate their first-half form after the break.
"I felt our first half was pretty good," said Wyles.
"We were pretty happy with that in a way. But we let ourselves down in the second half. That being said, Australia's a good team."
Australia took advantage of American lock Greg Peterson being sinbinned early in the game with tries to fly-half Bernard Foley and scrumhalf Nick Phipps.
The U.S. hit back with a penalty by Irish-born A.J. MacGinty and a try by scrum half Mike Petrie to get within striking distance at the break and raise hopes of an upset.
Michael Cheika's side did not concede any points in the second half, though the Americans came close several times before committing basic turnovers that the Wallabies pounced on.
Australia start their World Cup in Pool A against Fiji on Sept. 23, while the U.S. begin their Pool B campaign three days earlier against Samoa.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Greg Stutchbury)
