Skipper Rohit Sharma top-scored with a rapid 76 but it was KL Rahul's unbeaten 34 in the nerve-shredding final overs that helped India chase down a tricky 252-run target with one over to spare.
New Zealand fought tooth-and-nail defending a modest total of 251-7 and Michael Bracewell produced a memorable all-round display. But reigning Twenty20 world champions India could not be denied a second successive global title.
"It's been amazing," India batter Virat Kohli said after their tense victory.
"We wanted to bounce back after a tough tour of Australia. We wanted to win a big tournament and that's what we've ended up doing."
Daryl Mitchell made 63 and Bracewell contributed an unbeaten 53 but India could have restricted New Zealand to a lower total had it not been for four spilt catches.
After just one four in the first 21 balls, New Zealand opener Rachin Ravindra (37) cut loose and appeared to have Lady Luck on his side.
Mohammed Shami spilled a return catch from the opener while Shreyas Iyer spilled one in the outfield to give Ravindra a second respite.
Spinner Varun Chakravarthy broke the 57-run opening stand when he trapped Will Young lbw for 15.
Rohit introduced Kuldeep Yadav after the powerplay and the left-arm wrist-spinner responded by clattering Ravindra's stump with his first delivery.
In his next over, Kane Williamson spooned a return catch to the curly-hair spinner and India were cock-a-hoop having seen the back of New Zealand's batting mainstay.
Axar Patel and Ravindra Jadeja applied the squeeze but India continued to drop catches with captain Rohit and his deputy Shubman Gill being the culprits.
Chakravarthy returned to remove the dangerous Glenn Phillips (34) and Mitchell fell to Shami just when he looked prime to launch a late assault.
India's spin quartet bowled a combined 38 overs conceding only 144 runs to give their team complete control of the middle overs while also claiming five wickets.
Having lost the service of pace spearhead Matt Henry through a shoulder injury, New Zealand bowlers had their task cut out and Rohit led India's powerplay assault.
New Zealand skipper Mitchell Santner opted for spin from both ends but Rohit and Shubman Gill (31) went on to forge the tournament's first opening stand of 100 or more.
Phillips plucked a one-handed blinder to dismiss Gill and Bracewell removed Virat Kohli with his first delivery to peg back India.
With boundaries drying up, player-of-the-match Rohit charged out against Ravindra only to be stumped - his dismissal injecting fresh excitement into the contest.
Iyer (48) combined with Axar Patel (29) to steady India but New Zealand kept prising out wickets.
Despite the madness around him, Rahul batted with ice in his veins to take India closer to the target and Jadeja sealed their victory with a four.
"Obviously it is bittersweet," player of the tournament Ravindra said.
"It was a great final, we played some great cricket in the lead-up...
"Individual accolades are great but the build-up to the tournament and playing for a great team was very enjoyable."
