Emerging star Cameron Green held his nerve with a career best 89 not out in Australia's thrilling two-wicket victory over New Zealand in the first one-day international on Tuesday in Cairns.

After Glenn Maxwell starred with four wickets and a spectacular catch to restrict New Zealand to a modest 232-9, Australia slumped to 44-5 against inspired new ball bowling from quicks Trent Boult and Matt Henry under lights.

A composed Green and Alex Carey (85) turned the match on its head with a brilliant 158-run partnership to overwhelm an increasingly ragged New Zealand attack.

But Carey's dismissal in the 40th over triggered a late twist as Australia crashed to 207-8 and still needing 26 runs, a target made more difficult with Green in discomfort with cramps.

Green, however, would not be denied as Australia sealed victory in an anti-climax through a wide delivery from quick Lockie Ferguson to start the 46th over.

Australia drew first blood in the three-match Chappell-Hadlee series, which continues at the same venue on Thursday.

"It was an amazing effort in his 11th (ODI) game to play a match-winning knock," Australia skipper Aaron Finch said of 23-year-old Green.

Australia's batting order appeared set for another humiliating performance in the wake of being dismissed for a lowly 141 in a stunning three-wicket loss to underdog Zimbabwe on Saturday.

Their chase started disastrously when under-pressure Finch fell lbw to Boult for five.

The 35-year-old opener unsuccessfully reviewed the decision and trudged off with his ODI career seemingly hanging in the balance having scored just 26 runs in his last six matches.

Left-arm quick Boult was on a roll when he dismissed in-form Steve Smith and recalled Marnus Labuschagne then Henry took over to leave Australia teetering before Green and Carey produced a record sixth-wicket partnership for Australia against New Zealand in ODIs.

"It ebbed and flowed. We weren't able to get that extra breakthrough after they were five down early," said captain Kane Williamson as New Zealand's 13-year drought in ODIs against the home team in Australia continued.

After Finch won the toss and chose to bowl, Maxwell's part-time off-spin stole the show as New Zealand's batters failed to convert starts with Devon Conway (46), Williamson (45) and Tom Latham (43) falling short of half-centuries.

Maxwell's purple patch started when he brilliantly caught veteran opener Martin Guptill one-handed in the gully in the fifth over before he took over with the ball.

The day-night contest ended an 18-year drought of international cricket in Cairns.

Australia v New Zealand first ODI scores

Brief scores from the first one-day international between Australia and New Zealand in Cairns on Tuesday:

New Zealand 232-9, 50 overs (D. Conway 46, K. Williamson 45, T. Latham 43; Glenn Maxwell 4-52, J. Hazlewood 3-31)

Australia 233-8, 45 overs (C. Green 89 not out, A. Carey 85; Trent Boult 4-40, Henry 2-50)

Result: Australia win by two wickets