India have dominated the opening hour on Day 2, scoring 77 runs from 14 overs bowled.
Pant and Gill have put on 79 runs for the fifth wicket from 87 balls to put the hosts in control. They now trail New Zealand by 72 runs.
New Zealand will also rue putting down the catch of Gill at a crucial juncture when he was on 45, putting down by substitute Mark Chapman off the bowling of Glenn Phillips.
Pant has dominated, hitting 50 from 48 balls, with seven fours and two sixes, while Gill has made 58 from 75 balls.
Their positive approach has ensured India have maintained a net run rate of nearly five, as India look in control on 163/4 in 33 overs.