Chasing 157, Australia's captain took complete control of the contest with a stunning unbeaten 103 from 52 deliveries, striking seven sixes and nine fours. With little support from the other end, Mitchell Owen's 14 was the next-best contribution,
Marsh's lone hand proved decisive as Australia reached 160 for seven in the 18th over.
New Zealand's bowlers fought hard to defend their total. Jimmy Neesham was outstanding with 4 for 26, troubling Australia's middle order, while Jacob Duffy chipped in with 2 for 29. Yet neither could contain Marsh, who refused to let the chase slip away.
Earlier, the Black Caps set 156 for nine, a total built around Tim Seifert's 48 from 36 balls. Michael Bracewell (26 off 22) and Neesham (25 off 18) added valuable runs, but Australia's attack kept the scoring under control.
Sean Abbott impressed with 3 for 25, while Josh Hazlewood and Xavier Bartlett collected two wickets apiece to prevent New Zealand from building real momentum.
Australia stumbled to 134 for seven at one stage, with Travis Head (13), Tim David (15), and Marcus Stoinis (5) all falling cheaply. But Marsh's composure under pressure carried them home in a tense finish.
The result underlined Australia's dominance in the series, after the opening win in Wellington and the washout in Auckland. More than that, it highlighted Marsh's commanding influence.
His century, only the second of his T20I career, ensured the series would be remembered for his brilliance with the bat.
Match Summary
New Zealand 156/9 (20 overs): Seifert 48; Abbott 3-25
Australia 160/7 (18 overs): Marsh 103; Neesham 4-26
Australia won by 3 wickets, series 2-0
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