After a slowish opening half, the contest sparked into life in the second spell as play flowed one way then the other.
Australia played most of the match with an undermanned bench, with second rower Luke Lewis helped off midway through the first half with an ankle injury.
They were also without centre Brent Tate, and the early medical assessment was a depressing one for the former New Zealand Warrior.
The North Queensland-bound Tate, who has already had two serious knee injuries in his career, appeared to have suffered another one.
Australia opened the scoring in just the third minute with a try that replays showed followed a movement that should have been halted.
Tate put his foot in touch in a tackle from former club team-mate Simon Mannering, who was inserted into the backline after Junior Sa'u pulled out with corked thigh.
But the officials failed to pick it up and, as the Kangaroo attack continued, skipper Darren Lockyer's kick into the in-goal evaded opposition fullback Lance Hohaia.
On hand to touch down was none other than Tate, with Cameron Smith adding the conversion.
New Zealand gradually got themselves into the match, with some solid defence.
There was also some good impact off the bench from prop Greg Eastwood, with a couple of strong runs.
It was also Eastwood's charge-down of Lockyer's kick that gave New Zealand field position that led to their opening try.
Not surprisingly, it was Marshall who played an instrumental role, his short ball putting centre Shaun Kenny-Dowall into a hole and over.
Marshall added the extra to tie the scores.
There were some fireworks after the halftime hooter with Kiwi Adam Blair and opposite number David Shillington squaring off in a melee that brought other players in.
The Kiwis came out the stronger after the interval, hooker Issac Luke starting to find holes around the ruck.
But it was the Kangaroos who hit the front again off a Kiwi mistake.
From the ensuing possession, and helped by a piggy back penalty, the home side swept downfield.
Bird's offload led to fullback Bill Slater crossing over midway through the spell, with Smith landing the sideline conversion.
The game blew up again with 15 minutes to go when Smith retaliated to a push from Bird, but referee Tony Archer ruled the penalty against Bird.
It was the first of three quick penalties for the Kiwis close to the Kangaroo line, but they couldn't take advantage.
However, with nine minutes to go, New Zealand did strike, a Marshall kick behind the defensive line pounced on by winger Jason Nightingale, who dotted down.
Marshall's angled conversion attempt the up-right and bounced back.
But the five-eighth sparked the long-range attack that provided the winner.
His break lead to Nightingale streaking down the touchline, and Marshall was again involved as his over-the-head pass found Fien.
