Jamieson, who is 2.03 meters tall, first made 25 in an unbroken partnership of 76 with Ross Taylor (73 not out) for the ninth wicket which helped New Zealand recover from a damaging middle-order collapse.
He then claimed the early wicket of young star Prithvi Shaw and bowled 10 overs to finish with 2-42 as New Zealand defended a moderate total of 273-8, dismissing India for 251 with nine balls to spare.
Jamieson's final contribution was to break a troublesome 76-run partnership for India's eighth wicket between Ravindra Jadeja (55) and Navdeep Saini (45) which threatened to swing the match India's way. The partnership carried India within 44 runs of New Zealand's total before Jamieson bowled Saini in the 45th over.
"It's still sinking in, I guess, with the bat and then with the ball," said man-of-the-match Jamieson. "The game kind of ebbed and flowed so it was nice to be on the right side of it."
Jamieson made his long-delayed international debut for a New Zealand team which was leading the three-match series 1-0 after a four wicket win in the first match at Hamilton but entered the match with problems of its own.
A stomach bug swept through the New Zealand camp around midday, ruling allrounder Mitchell Santner and fast bowler Scott Kuggeleijn out of the match. Tim Southee was also struck down but played on, bowling his 10 overs and taking 2-41.
Jamieson has been around the team all season but had to wait for his debut, sitting out New Zealand's 3-0 test series defeat in Australia and its 5-0 loss to India in the Twenty20 series. He was finally given his chance on his home ground at Eden Park and made an immediate impression.
In spite of his height Jamieson doesn't bowl at express pace, averaging around 130 kph. But the trajectory he creates from a high-release point creates difficulties for batsman. He is also a better than average tail-end batsman with three first-class 50s.
He played a small but vital role on Saturday. New Zealand seemed likely to fall short of a competitive total even after Martin Guptill and Henry Nicholls put on 93 for the first wicket after India won the toss and chose to field.
Nicholls made 41 and Guptill 79 but from 141-1 in the 26th over — heading for a total in excess of 300 - New Zealand lost its next seven wickets for under 50 runs as spinners Ravindra Jadeja and Yuzvendra Chahal helped India apply the squeeze.
In came Jamieson for his first international innings and he stuck around with Taylor who followed his match-winning century in the first match of the series with an unbeaten 73. Jamieson's 24-ball innings included two sixes.
Shaw began India's chase in spectacular fashion, striking two fours from the first two balls and three from the first four. He reached 24 entirely in boundaries before Jamieson beat him between bat and pad to end a dangerous innings.
Southee did the same to India captain Virat Kohli, bowling him for 15 to substantially boost New Zealand's winning chances.
Shreyas Iyer followed his first ODI century with a half century from 56 balls but he was out next ball as India's middle order crumbled. K.L. Rahul (4) and Kedar Jadhav (9) were also out cheaply.
Jadeja's half century from 67 balls and his long stand with Saini revived India's hopes but the end came quickly after Saini's dismissal.