Australia chose to bat first, and the surprise decision from captain Mitchell Marsh was vindicated as they scored 294-8 in their 50 overs, setting Zimbabwe an imposing target at Harare Sports Club.
In reply, Zimbabwe were dismissed for 235 in 45.1 overs, showing good fight but always behind the required run rate.
Renshaw, who last scored an international ton in a test against Pakistan in 2017, made 109 and featured in key partnerships after Cooper Connolly survived a few let-offs before being bowled by Zimbabwe captain Sikandar Raza for 51.
Renshaw put on 72 runs with Alex Carey for the fifth wicket and 75 with Ollie Peake for the sixth wicket, leaving Zimbabwe with a required run rate of 5.90.
The 20-year-old left-arm quick Newman Nyamhuri finished with 5-62, only the second Zimbabwe bowler to take five wickets in an ODI against Australia.
Zimbabwe lost four wickets quickly before Craig Ervine and Sikandar steadied the innings with a 98-run partnership that offered them hope of victory on a surface that traditionally gets better for batting as the day wears on.
Nathan Ellis had taken two wickets in his first spell, and when he was reintroduced, took three balls to clean bowl Ervine for 59 and put the brakes on the home side. Sikandar was yorked by Spencer Johnson for 57 to leave Zimbabwe still significantly adrift.
Ellis finished with 5-31 in 9.1 overs, also cleaning up the tail.
The second ODI is on Friday, and the last on Sunday, all in Harare, after which Australia moves onto a similar series with neighbouring South Africa.