The visitors were 85/4 in reply to India's first innings total of 316, with stand-in skipper Ross Taylor (30) in the middle, as early tea was taken due to rains after Luke Ronchi (35) departed in the fourth delivery of the 20th over about 80 minutes after lunch.
The drizzle left the outfield soggy and the covers were rushed in.
New Zealand were 231 runs adrift of India, whose first essay ended 87 minutes into the pre-lunch session.
The visitors lost their third wicket in the second over of the post lunch session, with Henry Nicholls (1) inside edging a back-of-the-length delivery on to his stumps to give Bhuvaneswar Kumar his second success.
New Zealand were precariously placed at 23/3 and could have suffered a further setback some time later had Gautam Gambhir not dropped an attempted cut from Ronchi at short point.
Ronchi, who had earlier punished a short delivery from Shami for a six over square leg, was on 16 when he got his life. The visitors' score read 52, with Shami being the unlucky bowler.
At the other end, Taylor looked composed, realising the onus of rescuing the Kiwi boat lay mostly on his shoulders.
Spin was introduced in the form of Ravichandran Ashwin in the 16th over, but Ronchi welcomed him with a boundary past thirdman, before Taylor joined in the act executing a sweep past square leg into the fence that also brought up the 50 of the partnership.
Taylor proceeded to cover drive the next delivery again into the ropes, as Ashwin's first over cost 13 runs.
Ronchi departed to a debatable leg before decision, when he played half forward to Ravindra Jadeja and was rapped on the pad. The hawkeye showed the ball would have missed the stumps.
The fourth wicket stand between Ronchi and Taylor was worth 62.
In the morning, local boy Wriddhiman Saha added gloss to his growing reputation of scoring vital runs in the lower-order, remaining unbeaten on 54 as the hosts recovered from an early jolt on day one to put up a par total on a trying wicket.
For the visitors, pacer Matt Henry was the pick of the bowlers returning figures of 3/46 with Trent Boult, Neil Wagner and Jeetan Patel bagging two wickets each.
Preferring the off-side, Saha hit seven fours and two sixes en route to his half-century which he scored in 109 minutes.
Overnight batsman Ravindra Jadeja fell for 14, while Bhuvneshwar Kumar and Mohammed Shami also did not last long.
New Zealand batsmen struggled to cope with the swing and guile of Bhuvneshwar and Shami as both openers Tom Latham (1) and Martin Guptill (13) fell in quick succession.
The tourists were 21/2 at lunch
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