New Zealand scored 348 in their first innings as Ishant Sharma (5/68 in 22.2 overs) remained the stand-out bowler for India.
Ravichandran Ashwin (3/99) got a couple of wickets in the morning session but not before getting a lot of stick from the tail-enders including Jamieson and Boult.
Jamieson's 45-ball knock had four towering sixes and he added 71 runs for the eighth wicket with Colin de Grandhomme (43 off 74 balls) in under 15 overs.
Boult (38 off 24 balls) had some real fun in the end and by that time, the shoulders of the Indian attack had already drooped as they were able to read the writing on the wall.
Jamieson and Boult were the reasons that New Zealand could extend their lead above 175-run mark as India will now have to play the catch up game.
The day started on a bright note as Jasprit Bumrah (1/88 in 26 overs) removed the normally dogged BJ Watling (14) off the very first delivery of the morning session, caught by Rishabh Pant.
Ishant was a bit lucky when Tim Southee chased a wide delivery outside leg stump, only to hit it straight to Mohammed Shami at fine leg.
At 225 for 7, just when it looked that India will keep the lead under 100, Jamieson used his reach to smother Ashwin's spin and height to pull the bouncers from Indian pacers, shattering the confidence of the visiting team attack.
The last wicket stand of 38 between Boult and Ajaz Patel only added insult to the injury. By the time Ishant completed his 11th five-wicket haul in Tests, there was little to cheer for the Indian team.