Ravichandran Ashwin (9 not out) and Ravindra Jadeja (4 not out) were at crease when the teams walked off for the short break, and India, chasing 359, are still in need of 181 runs.
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In the second innings, India lost wickets in a heap on a rather biting pitch against Santner after making a confident start to their chase, courtesy conditions-defying 77 from opener Yashasvi Jaiswal off just 65 balls.
His 62-run alliance for the second wicket with Shubman Gill was the finest phase of the Indian essay.
Earlier, the Kiwis were bowled out for 255 in their second dig after resuming from 198 for five.
Brief scores: New Zealand: 259 and 255 all out in 69.4 overs (Tom Latham 86, Glennn Phillips 48, Tom Blundell 41) vs India: 156 and 178/7 in 40 overs (Yashasvi Jaiswal 77; Mitchell Santner 5/72).