Running out of batting partners, Green brought up his second Test ton on the penultimate ball of the day, smashing rookie seamer Will O'Rourke past backward point to the fence as Australia went to stumps at 279 for nine at the Basin Reserve.
The all-rounder survived the final ball to march off unbeaten on 103, with tailender Josh Hazlewood yet to score.
"It obviously feels pretty good ... It was a pretty tough wicket out there," said Green, who kissed the crest on his helmet after bringing up his hundred.
"I thought the boys played pretty well.
"It was nice to kind of stick out there and hopefully put a semi-competitive total on the board."
Green's century and a rollicking, 132-run final session ensured Australia narrowly took honours on a pulsating day one, having been sent in to bat on a green-top pitch after home captain Tim Southee won the toss.
Matt Henry took four wickets, while Scott Kuggeleijn took two victims as the fourth seamer, with selectors opting for more pace rather than the slow-bowling all-rounder Mitch Santner.
New Zealand's bowlers swung the ball menacingly but were sometimes wayward and ultimately expensive, racking up 30 runs in extras for the day as balls repeatedly ballooned over wicketkeeper Tom Blundell for byes.
They also laboured fruitlessly in the morning as openers Steve Smith and Usman Khawaja held firm until the verge of lunch.
Henry eventually broke through by having Smith caught behind for 31, ending a 61-run partnership.
Rejuvenated after the break, New Zealand's quicks tore through Australia's top order in an electrifying hour.
Shackled by tight line-and-length bowling, the out-of-form number three Marnus Labuschagne made only one run from 27 balls, edging Kuggeleijn to first slip.
Khawaja followed soon after for 33, his stumps shattered by a peach of a delivery from Henry, while Travis Head, coming off a pair of ducks from his previous test, was caught behind for one off the bowling of O'Rourke.
Green survived, though, building a 67-run partnership with Mitchell Marsh, who came out swinging in a 39-ball 40 before he was caught top-edging Henry with a botched pull-shot.
Australia were 176 for six soon after tea, when wicketkeeper Alex Carey tossed his wicket away for 10, driving Kuggeleijn straight to Kane Williamson's safe hands.
Yet Green went on the offensive and foiled New Zealand's hopes of rattling through Australia's batters in a day.
The towering all-rounder anchored valuable partnerships with tailenders Mitchell Starc (9) and Pat Cummins (16) and moved into the nineties with Nathan Lyon.
Henry produced another brilliant ball to have Lyon caught behind for five, though, leaving Green's hopes of a century in peril.
The number four responded by thrashing two fours off O'Rourke to move to 99, then a third to reach his hundred in style.
