India spinner Axar Patel struck three times in the post-lunch session to restrict New Zealand to 249-6 on day three of the opening test in Kanpur on Saturday.
Replying to India's first innings total of 345, New Zealand were 197-1 in the morning session with opener Tom Latham approaching his hundred and skipper Kane Williamson in the middle.
After seamer Umesh Yadav removed Williamson on the stroke of lunch, spin duo of Patel and Ravindra Jadeja claimed a combined four wickets to wrest the initiative for the home side.
Tom Blundell was on 10 at the tea break, and Kyle Jamieson on two with New Zealand still 96 behind at the Green Park Stadium.
Patel (3-46) hurt New Zealand in the second session when he removed veteran Ross Taylor (11) with Bharat taking a sharp catch behind the stumps.
Latham made 95 before stepping out against Patel only to be stumped after a fine knock that included 10 boundaries.
He also claimed the wicket of Henry Nicholls while fellow left-arm spinner Jadeja dismissed debutant Rachin Ravindra to boost India's hopes of taking a handy first-innings lead.
Earlier in the morning, Ravichandran Ashwin finally ended India's 66-over wait for a first wicket, snapping New Zealand's 151-run opening stand in the process.
Will Young, having made a career-best 89, edged Ashwin and substitute wicketkeeper KS Bharat - replacing Wriddhiman Saha who was being treated for a stiff neck - grabbed a low catch behind the stumps.
Young was initially ruled not out, but India reviewed that decision, which had to be overturned after replays confirmed the edge.
Young's fine knock included 15 boundaries.
Soon after India took the second new ball, Yadav trapped Williamson leg before wicket.
Williamson, who made 18, reviewed the decision, but replays confirmed the ball would have hit the top of his middle stump.
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