The victory in its 500th Test in Kanpur meant that India is now one victory away from reclaiming the ICC Test Championship mace from Pakistan. India had entered the three-match series against the Kiwis, trailing Pakistan by one point and needed to win the series to move ahead of its traditional rival.
Off-spinner Ravichandran Ashwin, who was the star of the Kanpur win, also climbed one place to occupy second position in the ICC Test Rankings among bowlers.
Another strong performance in the Kolkata Test, which starts on Friday, will potentially see Ashwin top the bowling charts for the second time this year after first claiming the number-one position last year following the Boxing Day Tests.
New Zealand captain Kane Williamson also climbed up one place each to occupy second position among batsmen. Williamson has edged England's Joe Root by one point with innings of 75 and 25 to reach 879 points. Australia captain Steve Smith leads the rankings with 906 points.
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Ashwin also contributed with a useful innings of 40 to consolidate his position at the top of the list of all-rounders. Ashwin has reached a career-best rating of 450, opening up a 66-point gap with second-placed Shakib Al Hasan of Bangladesh.
There was not much to cheer for other New Zealand batsmen apart from Williamson, but for India, opener Murali Vijay and Cheteshwar Pujara made significant gains.
Vijay and Pujara, who became the first Indian pair in 10 years to notch century partnerships in both innings of a Test match, moved up from joint-20th position to joint-16th position.