Resuming at 130 for four, India were bowled for 202 to concede a first innings lead of 301 runs as overnight batsmen Rohit Sharma (72) and Ajinkya Rahane (26) failed to provide the side a good start.
The hosts did not enforce a follow-on on the Indians, hoping to bury the visitors under a mountain of runs but the ploy failed as Indians bounced back brilliantly to bundle out the Kiwis for 105 runs in 41.2 overs on an eventful third day, which saw as many as 17 fall at the Eden Park.
Pacemen Mohammed Shami (3/38) and Ishant Sharma (3/28) dismissed three batsmen each while Zaheer Khan (2/23) scalped two wickets to bring India back in the game.
India were 87 for one at close, stilling needing 320 runs for a remarkable victory and with two full days left in the game, a result is almost certain.
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Opener Shikhar Dhawan (49), who survived an LBW appeal of Ish Sodhi off the last ball of the day, and Cheteshwar Pujara (22) were at the crease for the visitors.
West Indies hold the incredible record of chasing 418 against Australia in May 2003 at St John's. Only thrice a target in excess of 400 has been chased till date.
India are second in the list with the successful chase of 406 runs against the Caribbean side but it was way back in 1976. Australia are third team to record a win while chasing a 400-plus score when they scored 404 against England in 1976.
He trapped Hamish Rutherford leg before for a first-ball duck off the last ball of the very first over of the innings. And two overs later, he had Peter Fulton (5) caught driving at cover, where Jadeja took a regulation catch.
Jadeja was once again in action in the sixth over, when he took a screamer of a catch to send back in-form Kane Williamson, off Zaheer.
Jadeja was not done yet as he ran out the New Zealand skipper Brendon McCullum (1) in another brilliant fielding display. McCullum was given a life in the eighth over, when Murali Vijay dropped a dolly at first slip.