Williamson registered his 33rd Test fifty scoring an unbeaten 52 while Taylor scored 47 runs as the Kiwis registered the big win. The winning runs came off Taylor's bat as he flicked a delivery of pacer Mohammed Shami towards deep square leg fence for a boundary.
The foundation was laid by Tim Southee, who starred with the ball by picking up four wickets earlier on Wednesday. India were bowled out for 170 in their second innings, setting New Zealand a target of 139 in 53 overs.
The Blackcaps openers Tom Latham and Devon Conway saw off the new ball but were dismissed by Ashwin which gave India a glimmer of hope.