Barring Cheteshwar Pujara (87) and Ajinkya Rahane (77), none of the batsmen came good after skipper Virat Kohli opted to bat on the relaid pitch of the historic Eden Gardens stadium, hosting India's 250th home Test.
Ravindra Jadeja (0) and Wriddhiman Saha (14) were holding fort for the home side when stumps were drawn at the end of the 87th over due to bad light.
Medium-pacer Matt Henry was the Black Caps top wicket-taker with a haul of 3/35 in his miserly 15 overs, while off-spinner Jeetan Patel, brought into the side due to the injury-forced exit of Mark Craig, chipped in with two wickets.
India, who will regain the top spot in ICC rankings if they seal the three-match series in this match, did not make a very good start and lost their top-three batsmen even before the score had touched 50.
For the in-form Pujara, it was his third half-century from as many innings but a lapse in concentration ended his patient innings for 87 that came off 219 deliveries and was studded with 17 hits to the fence.
From being 46/3 in a jittery first session, Pujara and Rahane batted with grit and determination under the blazing afternoon heat and energy-sapping humidity.
The duo's stand spanned three hours and nine minutes but the Kiwis made an impact in the final session snapping four wickets.
(REOPENS DEL 48)
For the Kiwis, it was a tale of two comeback men as first 24-year-old Henry (3/35), who had replaced their pace spearhead Tim Southee created quite a flutter by removing both the openers -- Shikhar Dhawan (1) and Murali Vijay (9).
Off the second ball of his first over, Henry bowled Dhawan who tried to cut in an angled delivery only to drag the ball back to his stumps.
Continuing a rare lean patch, skipper Kohli (9) was steadying the ship with a set Pujara, but Trent Boult (1/33) dismissed the skipper.
Kohli got carried away after an exquisite cover drive that was cheered by the small turnout and went for an IPL-like shot chasing a ball way outside the off-stump to be caught brilliantly by Tom Latham.
The dismissal less than half an before the lunch break disturbed India's recovery plan before Pujara and Rahane held firm in the second session.
After aiding seam movement and offering variable bounce in the morning, the pitch turned slower on a sultry afternoon, offering occasional turn. However Pujara and Rahane batted sensibly to resurrect the innings.
They were never in a hurry and played according to the merit of the ball, collecting timely boundaries in the process.
Giving him a able support at the other end was Rahane, who hit 11 fours in his 157-ball stay at the crease. Rahane's resolute knock came to and end when Patel trapped him LBW with India exactly at 200.
