The 24-year-old from Christchurch, who replaced Ish Sodhi, dismissed Shikhar Dhawan (1) and Murali Vijay (9) in the first 50 minutes in his brilliant first spell of 6-2-14-2 as the Kiwis seamers utilised the grassy condition to full effect after Kohli opted to bat.
Just when it seemed Kohli (9) was steadying the ship with a set Cheteshwar Pujara, Trent Boult dismissed the skipper who continued his string of low scores.
The dismissal less than half an before the lunch break pegged back India's recovery plan and at the break Pujara was unbeaten on 31 and looked defiant with Ajinkya Rahane on two.
Earlier it was the tale of one comeback man cutting short another's when Henry dismissed Dhawan in the second over of the day.
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In the second ball of his first over, Henry, who, last played in February against Australia at Christchurch, bowled Dhawan who tried to cut in a high bounce angled delivery only to drag the ball on to his stumps.
Pujara got off the mark with two elegant boundaries on both the sides of the wicket with Vijay also looking in fine form before becoming the victim of a beauty from Henry.
Playing only in his fifth Test, Henry after repeatedly beating the outside edge bowled one straight and full delivery and Vijay had no option but to go for it as it took a faint edge down to BJ Watling behind the stumps.
(REOPENS DEL 17)
Kohli stuck to his four-bowling strategy but brought in seamer Bhuvneshwar Kumar in place Umesh Yadav while Dhawan replaced the injured Lokesh Rahul in two changes to India XI.
The Black Caps, however, were hit hard by their skipper Kane Williamson's illness as the Test number 2 batsman could not recover from fever in time and Ross Taylor stood in as captain.
Henry Nicholls replaced Williamson, while Matt and Patel came in for Ish Sodhi and Mark Craig in the three changes to their XI from Kanpur Test which they lost by 197 runs to trail the three-match series 0-1.
The giant silver-coated bell just below the Eden clock was installed on the lines of the five-minute Lord's Bell which was introduced in 2007.
Each morning the bell will be rung by different personalities to mark the start of play in the second Test.