Chasing 164, the Black Caps rode on a brilliant 84 not out from Seifert and unbeaten 57 from Williamson to comfortably chase down the target with four balls to spare.
"It looks to be a very good pitch and we want to get a good score on the board," said stand-in captain Shadab Khan.
With this win, the Kiwis have attained the number one ranking in Test cricket for the very first time. The side have also toppled England at the third spot in World Test Championship standings.
The former Kiwi speedster says Wagner could create problems to Indian batsmen
The Bengaluru franchise is optimistic of ending on a high in new season.
Williamson had suffered considerable discomfort while batting, although he managed to score 74.
This knock by the Kiwi captain has lifted him from 897 points to 915 points and he is just seven points away from toppling Virat Kohli at the top position in the ICC Test batsman rankings.
For Australia, Pat Cummins has been the pick, gaining five slots to reach a career-best third position after finishing with nine wickets in the match
The series is currently level at 1-1, with the New Zealand taking lead in the initial match and the hosts levelling things in the second.
12Page 1 of 2