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.

"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.

"I couldn't really walk for a second there. Groin, calf, hamstring and forearm – the whole lot was going. Not ideal but that's ok," Green told Fox Cricket after Australia's two-wicket win.

"He's a really calm character," Carey told reporters in Cairns on Tuesday.

"Bat and ball and in the field; (he) just goes about his business and he's really focused."

"And he does it in a way that I think we'll see him do it for a long time."

Australia take a 1-0 lead in the Chappell-Hadlee Trophy with the second match of the series to take place in Cairns on Thursday.