A century from Matt Renshaw set up the success in the first of three ODIs in Zimbabwe, which will be followed by three more in another 2027 ODI World Cup host country, South Africa.
After Mitch Marsh won the toss, the tourists made 8-294 from their 50 overs on Tuesday, with Renshaw leading the way with a 94-ball 109 - the highest score by an Australian in Zimbabwe.
Allrounder Cooper Connolly made 51 off 46 balls and there were decent contributions from Marsh (36 off 28) and young Victorian Ollie Peake (30 off 40).
Nathan Ellis was the key performer when Australia bowled, the Hobart Hurricanes' white-ball specialist taking a maiden ODI five-wicket haul and proving the most economical bowler.
After Zimbabwe slumped to 4-62 a 98-run partnership between veterans Craig Ervine (59) and Sikandar Raza (57) gave the hosts hope but once Ellis (5-31) bowled the former their challenge faded away, being all-out for 235.
"Important to start a three-match series with a win," said Marsh, standing in as skipper for the rested Pat Cummins.
"Matty's innings was brilliant. Got us to an above-par total. Nathan Ellis is a gem. I believe he's one of the best white-ball bowlers in the world. He can bowl in all phases and it's a privilege to have him in our side."
It could have been a different result had Renshaw not been dropped on 12. He took full advantage, twice hitting sixes onto the stadium roof, the second one bringing up his half-century.
And having failed to convert two fifties into centuries in his previous nine career ODIs, he went on with the job this time, raising his hundred with a single off paceman Brad Evans.
Renshaw's only previous international hundred was a memorable 184 in his fourth Test, back in 2017 against Pakistan in Sydney.
His Test career hasn't worked out as anticipated but he is in the squad for the forthcoming Tests in South Africa and this could provide the 30-year-old with the confidence to nail down a place on the Ashes tour. That would be personally significant as the English-born batter is yet to face the country of his birth in any format.
"I didn't feel under any scoring pressure. It was really nice. Pitch was nice. Ten years between international hundreds was not something I was expecting," he said.
Several Australians will hope to do better in the coming matches.
Travis Head chopped on, for the fourth successive innings, making four as did Josh Inglis, in his case off 12 balls. Alex Carey - selected as a No.5 batter while Inglis took the wicketkeeping gloves - laboured for 27 off 53 balls.
With the ball Adam Zampa's ten overs went for 55 with one wicket.
The leggie was the main bowler used as Marsh sought to dislodge the Raza-Ervine partnership. In a 16-over period seven bowlers were used with nine bowling changes, before Ellis was recalled and did the job.
It was Australia's first match in Zimbabwe for 12 years, when the hosts won. Marsh, Raza and Brendan Taylor were the three survivors with the latter becoming the longest-serving player in ODI history with his appearance.
His career has lasted 22 years and four months, eclipsing Sachin Tendulkar, and remarkable in that he retired in 2021, was then banned for breaching the ICC's Anti-Corruption and Anti-Doping codes, then came out of retirement last year after serving the suspension.
Cameron Green was left out of the playing XI due to shoulder soreness, while Josh Hazlewood also sat out with his workload being "managed".
Cummins and Mitch Starc will join the squad in South Africa for three more ODIs and the Test series.
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