De Grandhomme (43) and Jamieson put on 71 runs before the tall pace bowler was caught for 44, but their partnership ensured New Zealand built a healthy 183-run first-innings lead after India were dismissed for 165 on Saturday.
Boult was the last man out, with the session extended by 30 minutes as the last pair were at the wicket, for an entertaining 38 from 24 balls with Ajaz Patel left on four not out.
De Grandhomme and Jamieson had resurrected New Zealand's innings after they came together at 225-7 after Jasprit Bumrah and Ishant Sharma had provided a double breakthrough and put India in a strong position to keep the lead under 100 runs.
The hosts had resumed on 216-5 but BJ Watling was dismissed on the first delivery when he played at a lifting Bumrah ball and was caught by wicketkeeper Rishabh Pant for 14.
Tim Southee then flicked a Sharma delivery off his legs to Mohammed Shami at fine leg, turning India captain Virat Kohli into a fist-pumping, arm-waving whirlygig as he celebrated the early successes.
Kohli was even happier when de Grandhomme was given out lbw for seven shortly after by umpire Aleem Dar, but the batsman had the decision overturned on review and he then combined with Jamieson to turn the match back to New Zealand's favour.
Jamieson, who hit four sixes in his innings, was caught by Hanuma Vihari off Ravichandran Ashwin about 30 minutes before the scheduled lunch break at 1.30 p.m.
De Grandhomme was then caught by Pant from the off-spinner Ashwin with about 10 minutes to go, before Boult's cameo extended the session.
