Will Young missed out on Saturday on his maiden international century on day three of the first Test, but New Zealand were still in a strong position at 197-2 at lunch in reply to India's 345.
Kane Williamson fell leg-before to the second new ball to Umesh Yadav just before the break for 18 after a 46-run partnership with Tom Latham, still unbeaten on 82, in Kanpur.
Young started the day from his overnight score of 75 and looked assured before edging Ravichandran Ashwin to substitute wicketkeeper K.S. Bharat on 89 off 214 balls.
The 29-year-old hit 15 fours in a solid Black Caps reply after Tim Southee's five-for on the second day restricted India to 345 all out.
Openers Latham and Young had pushed the hosts on the defensive on Friday after a stand of 129 which was finally broken at 151 with Young's dismissal to Ashwin.
Latham survived a close call on 66 when stand-in captain Ajinkya Rahane -- stepping in for the rested Virat Kohli -- failed to review a leg-before appeal off Ashwin's bowling.
Ashwin was India's most effective bowler and has one wicket for 57 runs in his 28 overs on a wicket offering inconsistent bounce.
Jadeja bowled 20 wicket-less overs for 44 runs and Patel, the other Indian left-arm spinner, bowled 14 overs for 33 runs without a wicket.
Yadav, who took India's second new ball with Axar, has bowled 11.3 overs for 30 runs and Williamson's wicket. Sharma went wicket-less for 30 runs in his 12 overs.
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