New Zealand were set for their first 300 plus total of the series after Tom Latham (61) and Ross Taylor (44) laid the foundation with a solid 73-run stand for the third wicket.
Taylor's dismissal led to a flurry of wickets though New Zealand still managed to reach close to the 300 milestone, thanks to a valiant partnership between Neesham (57 off 47) and Henry (39 not out off 37).
For India, Amit Mishra and Kedar Jadhav were among the wickets again, taking two and three respectively. Pacer Umesh Yadav scalped three wickets as well but proved expensive, giving away 75 runs in 10 overs.
Here, after losing their seventh straight toss on the tour, New Zealand were expectedly put in to bat by India captain MS Dhoni considering the dew factor.
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With the ball coming nicely on to the bat, New Zealand were off to their best start of the series coasting to 64 for one in 10 overs.
Guptill, who had 171 runs in eight innings on this tour prior to today, began on a promising note. He hit Umesh Yadav on the up for a cracking four through point before dispatching Hardik Pandya for a comfortable six over long on.
The opener followed it up with another straight six over extra cover and a slash through point in Pandya's subsequent over.
The in-form Latham was batting patiently at the other end. He got into the act by pulling Yadav for a six. And just when it seemed Guptill was set to end his barren run, Yadav trapped him in front of the stumps with a fuller length ball that moved in sharply.
(REOPENS DEl 60)
Dhoni brought him ahead of specialist spinners and he was quick to repay his captain's faith, just like he did in the earlier games.
New Zealand needed a partnership to get going again. That was when Latham and Taylor stitched a solid 73-run stand to steady the innings. With pitch playing true and Taylor getting back among runs, first 300 plus score of the series was a straight forward task.
In Indian conditions, when Taylor gets cut shots right, one knows he is feeling good about his game. That is what happened today as he slashed and swept smoothly to go with a few lusty hits.
That wicket triggered a middle-order collapse for the second game in row and New Zealand found themselves reeling at 180 for 7 from a promising 151 for 2.
Mishra and Jadhav did the bulk of the damage as New Zealand's hopes of a formidable total were dashed in quick time. Mishra bowled another beauty to get Luke Ronchi stumped while Jadhav was a tad lucky to remove Corey Anderson off a full toss.