New Zealand, looking to sweep the series, posted an imposing 243 batting first in the third T20, the seventh highest innings of all time in the format.
Munro, with previous centuries against India and Bangladesh, moves ahead of four players, including the West Indies' Chris Gayle, on two T20 centuries.
His rollicking 104 off 53 deliveries included 10 sixes and three fours.
After New Zealand won the toss and opted to bat, Martin Guptill made a timely return to form in a century stand with Munro for the first wicket.
Munro hit Samuel Badree's first ball over the square leg boundary as New Zealand blasted away at 10-an-over.
Rayad Emrit, selected to make his T20 debut two months short of his 37th birthday, went for 16 in his first over with Munro slogging the first two deliveries for six.
But Emrit had the satisfaction of breaking the opening partnership with Guptill caught behind for 63 when New Zealand were then 136 for one in the 12th over.
Tom Bruce (23), Anaru Kitchen (9) and Kane Williamson (19) making short cameos before Munro was dismissed by Carlos Brathwaite in the final over.
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