Shreyas Iyer's calm head scripted victory for India with an over to spare.
Earlier, Williamson, Taylor and Munro scored half-centuries to propel New Zealand to 203.
Virat Kohli is set to play his first T20I in New Zealand.
During India’s last tour of New Zealand, the Indian bowlers restricted the Blackcaps under 250 in each of the five ODIs.
The Kiwis have lost seven out of their last eight T20Is at the Eden Park.
The tour of New Zealand is certainly India's toughest assignment post the debacle of the 2019 Cricket World Cup.
Apart from Kane Williamson, top-order batsman Henry Nicholls and spinner Mitchell Santner are also suffering from illness.
This was deemed to be the best chance for the Kiwis to end their 34-year drought down under.
Australia are clear favourites to continue their winning streak in the home summer.
It was yet another exceptional year for the cricketing folklore.