Third Twenty20, Wellington: New Zealand finished at 198/3 in 20 overs, with Daryl Mitchell making 89 from 52 balls and Singh taking 1-33.
India then chased down the target of 199/4 in 13.2 overs: Abhishek Sharma struck 113 from 38 balls, while Jamieson took 2-45.
India won by six wickets and took a 3-0 lead in the series.
Abhishek Sharma’s 35-ball century was the focal point of India’s rapid chase.
Sharma and teenage opener Vaibhav Sooryavanshi combined for 133 runs in seven overs during the first wicket, with their powerplay score of 118 setting a new international T20 record.
Fifteen-year-old Sooryavanshi’s 45 from 19 balls acted as a supporting innings to Sharma, who reached his fifty from just 15 deliveries as New Zealand’s bowlers struggled.
After Sooryavanshi was dismissed in the eighth over, Sharma helped India cruise toward their target, finishing with 113 off 38 balls, including nine fours and 11 sixes.
He fell short of equalling his own fastest T20 hundred, which he made off 30 balls against Afghanistan last month.
India then easily accounted for the remaining runs, with New Zealand captain Mitchell Santner taking 1-17 off three overs—a rare positive for the bowlers.
New Zealand’s 198/3 was set up by Daryl Mitchell’s 89 from 52 balls and Finn Allen’s 40 from 25, but India’s pursuit was largely controlled and powerful.
The result gave India an unassailable 3-0 lead in the five-match series, which will be followed by five one-day internationals and two Tests.