Brendon McCullum was batting on 39, while youngster Kane Williamson, who had a debut century in Ahmedabad during their last tour to India two seasons ago, was on 31 after bad weather delayed the proceedings by two hours in the morning.
Resuming the day on 41 for one, following on in their second innings, New Zealand added 51 runs to the overnight total with the duo putting on an unbroken 66-run partnership for the second wicket.
With nine wickets in hand, New Zealand still trail by 187 runs.
Earlier bad weather delayed the start of the match for the third time in as many days.
India began with the spin duo of Pragyan Ojha and R Ashwin but the Kiwi batsmen played them out sensibly.
McCullum and Williamson played with patience, waiting for the loose deliveries as India struggled to get a breakthrough.
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Their vigil at the wicket meant that the visitors put on their first 50 partnership of the match.
There was a setback for India when centurion Cheteshwar Pujara, while fielding at short leg in the 33rd over, was hit near his right knee around the same place he had a surgery last year.
Grimacing in pain, Pujara was taken off the field by the support staff before Ajinkya Rahane came in as the replacement.
India brought on medium-pacers Zaheer Khan and Umesh Yadav hoping for some reverse swing but there was no success with the Kiwi duo keeping their wicket intact.
Ojha continued his spell in the morning for 11 overs, conceding 17 runs with two maidens but a wicket eluded the Indians.