Left-arm spinner Mitchell Santner was the most successful among the Kiwi bowlers, returning figures of 2-60 off the 15 overs he has bowled so far.
Pacer Neil Wagner (1-34) also bowled well while Indian origin leg-spinner Inderbir Singh Sodhi (1-27) got the other wicket.
New Zealand pacer Trent Boult bowled well, producing appreciable swing and movement off the pitch, but was unable to bag a wicket.
For India, Ajinkya Rahane (12) and Rohit Sharma (0) were at the crease when tea was called.
Most of the Indian batsmen fell to poor shots after misreading the turn or bounce of the ball rather than any top quality bowling by the visitors.
The Indians started off on a positive note with opener Lokesh Rahul hitting Boult for a couple of boundaries in the very first over of the series.
The New Zealand pacers recovered thereafter to restrict the flow of runs to some extent.
Rahul however, continued to target Boult, hitting a couple of consecutive boundaries off the pacer in the seventh over.
The opener swept Santner for a six in the 11th over, but the spinner had his revenge off the very next ball when Rahul misread an outgoing delivery.
Rahul scored at a decent rate, posting 32 runs off 39 deliveries. His innings was studded with four boundaries and a six.
Cheteshwar Pujara then joined Murali Vijay in the middle and the duo negotiated the New Zealand bowling with skill and patience to ensure that the hosts went into the lunch break at a decent 105/1.
Santner was the only Kiwi bowler to bag a wicket in the morning session.
The rest of the Kiwi bowlers toiled away without reward under hot and humid conditions.
But whatever advantage the hosts had managed to claim was friterred away in the post lunch session as the Kiwi bowlers struck back to claim the crucial wickets of Vijay, Pujara and Indian skipper Virat Kohli.
Boult outfoxed Vijay in the very first over after lunch with cross-seam short pitched delivery. The Indian opener was surprised by the extra bounce as the ball took the outer edge of his bat and travelled to where first slip should have been.
But the lack of a fielder at that position saved Vijay and the Kiwis could only watch as the ball raced to the boundary.
Santner bagged his second wicket when Pujara misread the spin on a slightly overpitched delivery which did not turn much after pitching. Pujara played for the spin, expecting it to turn towards the offstump but only managed to offer a tame caught and bowled chance to Santner.
Kohli (9) seemed to be in good touch, hitting two boundaries during his short stay at the crease. But he fell to a rash shot, attempting to pull Wagner for a six. The Indian captain misjudged the bounce and the ball flew off the top edge for a relatively easy catch for Sodhi.
Earlier, Indian skipper Virat Kohli won the toss and elected to bat in the first Test of the three match series against New Zealand at the Green Park Stadium here.
India are contesting their historic 500th Test. The hosts are playing with six batsmen, two fast bowlers and two spinners while the visiting New Zealand are playing with three spinners and two fast bowlers.
India have played 14 Tests under Kohli’s captaincy so far, winning 10 of those. The hosts will be eager to register their 11th win under Kohli and make the historic 500th Test a memorable one for their fans.
India 185/4 (Murali Vijay 65, Cheteshwar Pujara 62; Mitchell Santner 2-60) vs New Zealand.