Chris Cairns' dismissal in the 47th over set up an match-winning partnership of 39 runs from 21 balls between No.5 Marshall and wicketkeeper Brendon McCullum.
That gave the battling Kiwis a four-wicket win with two balls to spare at Docklands stadium and the opening win in the inaugural Chappell-Hadlee Trophy series.
The Kiwis had lost their last seven One-dayers to the world champions and were also coming off a two-Test hammering from Ricky Ponting's crack team only a week later.
Marshall and McCullum lifted their side from an apparent unwinnable position to a certainty by plundering 22 runs off fast bowler Michael Kasprowicz in the 48th over.
"My job was just to hang in there, really, and just try to nudge around, get one a ball," Marshall said Monday.
"We always knew that if we've got wickets in hand with the big hitters coming in, we can have a good go at it.
"We knew if it was always around 10, even 12-13 off the last over, we were always going to have a dip."
Marshall was named Man of the Match for his unbeaten 50, which featured only one boundary, while McCullum smacked 20 from 13 balls.
Marshall's previous four One-day International scores were a duck against Australia in England, then seven, two and another duck against Bangladesh.
The second game in the best-of-three series is in Sydney on Wednesday, with New Zealand well-placed for an unlikely success over the world champions.
"It's going to take some doing, but you've got to get across the line more frequently to breed success and that's what we're excited about," Kiwi captain Stephen Fleming said on Monday.
"We're here and it feels damn good. I'm delighted we can turn it around so quickly and give ourselves a chance to win the series, but once again I'm still wary that we're still up against a very good side."
Another highlight was Mathew Sinclair's blinding one-handed diving catch to dismiss opener Matthew Hayden in Sunday's opener.
"Looking at conditions and the way we've tried to catch two-handed in our practice sessions, to take one like that...," Fleming said.
"It was also wet, quite wet, the ball was moving away, everything was against him catching it.
"You'd go pretty hard-pressed to find something better than that -- and the timing of it, as well, we were getting thumped once again (early in the Australia innings). It was a pretty special turnaround."