In easily his finest moment as an Australian cricketer, Marsh pounded an unbeaten 77 from 50 balls to help chase down the Black Caps' 4-173 with seven balls to spare in Dubai.
David Warner also starred, his 53 from 38 deliveries helping him claim player of the tournament ahead of legspinner Adam Zampa.
But more importantly, a 92-run stand with Marsh for the second wicket set up the biggest chase in World Cup final history and ended a 14-year hunt for the T20 title.
"It's awesome, it really is," captain Aaron Finch said.
"There's been so much talk about this being the one that's been elusive to Australia.
"And to be fair we've probably underperformed in the past, if we're being honest with ourselves.
"We've had some great teams along the way, this team is pretty special.
"The camaraderie, the way everyone really cares for each other and looks after each other, looks out for each other is pretty special so it's awesome."
Australia's success was perhaps their most unlikely of any of their white-ball World Cup wins since their first in 1987, given their horror lead-up to the tournament with five straight series losses.
But in Marsh, they found an even more unlikely hero.
Often the target of harsh criticism, he appeared out of the international frame a year ago and had played just 15 T20s between 2011 and 2020.
But he finished the World Cup with an average of 61.66 and a strike-rate above 145, making for the most prolific year of any Australian in history.
And when Australia desperately needed a batter to produce after Black Caps captain Kane Williamson's 85 from 48 balls put the game in the balance, Marsh delivered.
He hit Adam Milne into the crowd at backward square first ball and followed it up with two more boundaries.
"I just wanted to get out there and have a presence," Marsh said.
He gave the same first-ball treatment Jimmy Neesham and Mitch Santner's opening overs, taking the game to New Zealand.
He finished the game with 10 boundaries - including four sixes - before a Glenn Maxwell (28 not out from 18) switch hit sealed the deal.
"We committed to (Marsh) batting No. 3 for a long time. He knew that," Finch said.
"Sometimes you just need a little bit of backing and you need some confidence from everybody else."
The big chase came after Josh Hazlewood had earlier been Australia's best with the ball, claiming 3-16 and sending down 14 dot balls in three powerplay overs.
But his bad drop of Williamson threatened to prove costly, when he put the New Zealand star down on 21 at fine leg.
It prompted an explosion from the Black Caps, as Williamson took 19 off that Starc over and 22 off another with the left-arm quick struggling to hit his length and finished 0-60.
Hazlewood, Pat Cummins (0-27) and Adam Zampa (1-26) were in comparison miserly, allowing Australia's batters to create history.