Sent in to bat in blustery overcast conditions, the 13th-ranked tourists were bowled out in 47.3 overs for 200. The total never threatened Australia's experienced batting unit, which accelerated to 201-5 with 99 balls to spare.
Sloppy fielding allowed Zimbabwe's fragile top-order to make a promising start, easing to 61-1 by the first drinks break with Innocent Kaia caught and bowled for 17 by Mitchell Marsh.
After Adam Zampa (3-57) spun two quick wickets, 21-year-old Wesley Madhevere (72) batted cautiously with skipper Regis Chakabva (31), sharing in a partnership of 63.
The lower-order capitulated spectacularly though, swinging wildly against Green (5-33), whose entire haul came from catches in the deep while the final four wickets combined for 12 runs.