Ojha removed Kane Williamson (17) and well-set opener Martin Guptill (53) as New Zealand reached 108-3 at lunch after electing to bat.[break]
Skipper Ross Taylor was unbeaten on 27 at the break with one six and two fours, while Daniel Flynn was seven not out.
New Zealand lost opener Brendon McCullum for no score in the second over before Guptill and Williamson steadied the innings with a 63-run stand for the second wicket.
But Ojha dismissed both the batsmen in his second spell, trapping Williamson leg-before and then having Guptill caught by Gautam Gambhir at mid-wicket.
Guptill, dropped on 17, hit eight fours in his 12th Test half-century in 26 matches.
India opened the attack in overcast conditions with Ojha, but struck through left-arm paceman Zaheer Khan who trapped McCullum leg-before with his fifth delivery.
The hosts had a chance to put more pressure on New Zealand, but Virat Kohli dropped Guptill at third slip off Zaheer.
Guptill played some attractive shots during his 79-ball knock, hitting seamer Umesh Yadav for three fours in an over before reaching his half-century with a boundary in the bowler´s next over.
Williamson, the only New Zealand batsman to score a half-century in the opening Test in Hyderabad, hit two fours in his 44-ball knock.
India retained the side that won the opening Test by an innings and 115 runs, while New Zealand brought in fast bowler Tim Southee in place of Chris Martin.
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