At 154 for one, India were set for a big first innings total but, after Santner grabbed three top and middle-order wickets, Boult (3-57) claimed three in nine deliveries with the second new ball to peg back the hosts at Kanpur's Green Park Stadium.
Unsurprisingly, New Zealand's three spinners bowled the bulk of the overs to share five wickets on a typical sub-continental track which had little to offer the pacemen.
Ravindra Jadeja (16) and Umesh Yadav (eight) will return on Friday looking to take India, who went into the match with four bowlers to accommodate an extra batsman, past the 300-run mark.
"After losing the toss, I think we are reasonably positioned," Santner told reporters.
"We didn't try anything different. We tried bowling in the good areas to build pressure and tried getting wickets. It didn't spin early on but 291-9, not too bad."
Rahul's last four innings in all formats had yielded two centuries and a fifty and the right-hander, chosen ahead of Shikhar Dhawan, dominated his 42-run stand with fellow opener Vijay.
The 24-year-old hit four boundaries, and a six off Mitchell Santner, before getting a faint edge to wicketkeeper BJ Watling in the left-arm spinner's second over.
Cheteshwar Pujara (62) then joined forces with Vijay (65) to prop up the innings, the duo adding 112 runs for the second wicket and rarely looking in any discomfort.
They brought up their individual fifties in successive overs before Santner had Pujara popping a simple return catch.
After 11 overs of toiling on an unresponsive pitch, Neil Wagner struck a body blow when he banged it short and enticed Kohli (nine) to attempt a pull shot early in his innings, only for the right-hander to top edge a catch to Ish Sodhi.
India-born Sodhi dismissed Vijay just before tea with Watling holding on to another faint edge as New Zealand claimed three important wickets for 80 runs in the second session to halt India's progress.
Batting at six, Rohit Sharma made a fluent 35 but has not fully shown that he can replicate his limited-overs success in the longest format.
Ravichandran Ashwin made 40 but will be expected to make a greater impact with his off-spin bowling in conditions that should suit him.
Vijay was confident a score in the region of 300 would be enough for his team.
"I think we are in a good position," the right-hander said. "We have put the runs on the board. So all we've got to do now is go out there and put pressure on them while bowling. It's a good total to play around with."