Playing only his second test, Jamieson followed his 5-45 in India's first innings of 242 with his highest test score of 49 which lifted New Zealand to 235 when its first innings ended just on tea.
Jamieson made 44 and took 4-39 in the debut test at Wellington which New Zealand won by 10 wickets last week to lead the two-match series.
His innings Sunday and his 51-run partnership for the ninth wicket with Neil Wagner (21) helped rally New Zealand after it had collapsed from 63-0 at the start of play to 177-8, faced with the prospect of a first innings deficit. Jamieson was the last man out, falling just short of a maiden test half-century and with New Zealand only seven runs behind.
India's seam blowers produced an outstanding performance in responsive conditions Sunday to lead their team's comeback after they lost the toss and were dismissed for 242 in only 63 overs on the first day.
New Zealand had done well to reach stumps on the first day without loss but their innings crumbled Sunday, when they lost five wickets in the first session and went to lunch at 142-5. The collapse continued in the second session as they dipped to 153-7 when Jamieson came to the crease.
A former opening batsman at age group level, Jamieson showed correct technique and used his long stride to answer the seam and swing which had undone New Zealand's top and middle order. He seemed poised for a half century but was the last man out, skying a catch to wicketkeeper Rishabh Pant from the bowling of Mohammed Shami.
Shami took took 4-81 and Jasprit Bumrah 3-62 as they took advantage of extraordinary seam bowling conditions. On a surface which was harder and faster than the first day, the ball swung late and a long way and the New Zealand batsmen were at a loss to find an answer.
Spinner Ravi Jadeja also found conditions to his liking with the ball bouncing and turning and took 2-22. But he made a lasting impression with his breathtaking catch to dismiss Wagner from the bowling of Shami.
Wagner pulled the ball towards square leg and Jadeja leapt into the air, legs cycling more than a meter from the ground, and snatched the ball out of the air with his left hand at full stretch above his head.
The batsman stood gaping at the crease as the India fielders mobbed Jadeja as he stood smiling in almost equal disbelief.
"I just put my hand in the air and the ball stuck in my hand," Jadeja told Sky Sports. "I didn't even realize I'd caught it."