After captain Mitch Marsh won the toss, the tourists made 8-294 from their 50 overs in Harare on Tuesday, with Renshaw leading the way with a 94-ball 109 - the highest score by an Australian in Zimbabwe.
The Australians were tracking fairly at 4-107 when Renshaw entered the stage, and the Queensland left-hander set about shoring up the advantage by compiling his first ODI century.
He brought up his half-century with a mighty six onto the stadium roof over long-off from the bowling of left-arm spinner Wellington Masakadza.
And having failed to convert two fifties into centuries in his previous nine career ODIs, the 30-year-old went on with the job this time, raising his hundred with a single off paceman Brad Evans.
It came after a 76-run sixth wicket partnership with Oliver Peake (30) which lifted the Australians into the ascendancy by the late overs.
Renshaw eventually fell with five balls left in the innings, holing out to deep mid-wicket off 20-year-old left-arm quick Newman Nyamhuri, the pick of Zimbabwe's bowlers with 5-62.
Marsh began the innings solidly with 36 off 28 balls, carrying on after opening partner Travis Head (4) was bowled by Evans in the second over.
Cooper Connolly joined in a half-century partnership with his captain before Marsh was caught at cover.
Connolly was eventually bowled by leg-spinner Sikandar Raza after making 51 off 46 balls, with three sixes and four fours.
Alex Carey - selected as a No.5 batter while Josh Inglis took the wicketkeeping gloves - laboured for 27 off 53 balls. Inglis, batting at No.4, was caught behind for just four.
Marsh was one of three survivors from both teams who played in Australia's last ODI in Zimbabwe 12 years ago, which the host team won.
Zimbabwe skipper Raza and Brendan Taylor are the other two players who competed in that famous Zimbabwe victory in 2014.
Taylor became the longest-serving player in the history of ODIs with his appearance. His career has lasted 22 years and four months, eclipsing the previous longevity record of India great Sachin Tendulkar, who went for 22 years and three months.
Wicketkeeper-batter Taylor retired in 2021 and was banned for three-and-a-half years in 2022 for breaching the ICC's Anti-Corruption and Anti-Doping codes.
After serving the suspension he came out of retirement in 2025.
Cameron Green was left out of the playing XI due to shoulder soreness, while Josh Hazlewood also sat out as Australia went with three pace bowlers - Xavier Bartlett, Nathan Ellis and Spencer Johnson - in the first game of the three-match series.
The series is part of defending champion Australia's preparations for next year's World Cup.
Australia rested regular captain Pat Cummins for the three ODIs before he joins the team in South Africa for three one-dayers and the Test series.
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