A maiden five-wicket haul by seamer Cameron Green on Sunday set Australia up for a five-wicket victory in the first one-day international against Zimbabwe in Townsville, which is hosting the first series between the sides Down Under since 2004.

Sent in to bat in blustery overcast conditions, the 13th-ranked tourists were bowled out in 47.3 overs for 200. That total never looked troubling for 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.

"I just got a bit lucky at the end there, I was just at the right place at the right time," Green said.

"Trying to bowl back of a length on a wicket that was kind of going up and down I didn't really have to change what I was doing too much."

A tribute to former Australian cricketer Andrew Symonds, who died in a car accident outside Townsville in May, preceded the hosts' innings, which started emphatically with a boundary from the first ball.

David Warner and Steve Smith (48 not out) batted with freedom in pursuit of a low target after Aaron Finch departed for 15.

Warner survived a dropped catch on 36 off Sikandar Raza, and two balls later he walked after wicketkeeper Chakabva immediately reviewed for caught-behind.

However, the review was deemed to show insufficient evidence to overturn the not-out decision, causing the opener to trudge back out to the middle.

The off-spinner soon had his man though, clean bowling Warner for 57.

Australia's middle-order wobbled, conceding three wickets to Ryan Burl's leg-breaks, but Glenn Maxwell bludgeoned 32 from nine balls to seal the game.

The three-match series continues in Townsville on Wednesday.