Pacemen Matt Henry was the destroyer in chief to bring India to their knees on 24-4 after 10 overs, with key men Rohit Sharma and Virat Kohli dismissed for a single apiece.
Henry snapped Sharma's record run of form that included five centuries in a single edition of the World Cup to get the opener caught behind in his first over.
Veteran Trent Boult was also breathing fire and silenced a large Indian crowd to trap Kohli lbw on a delivery that swung back sharply from the left-arm quick.
Henry returned figures of 3-37 from his 10 overs as Mitchell Santner also provided able support to the paceman with his left-arm spin.
Santner got rising star Rishabh Pant and Hardik Pandya as he dried up the flow of runs in the middle overs.
Jadeja comes up just short
Ravindra Jadeja joined MS Dhoni with India tottering at 92 for six and almost dragged his side to victory with defiant effort that fell just short.
Veteran Dhoni was his usual calm self, but it was Jadeja's attacking 77 from 59 balls that gave India renewed hope just as the game was slipping away.
Jadeja, who also returned figures of 1-34 with his left-arm spin, put on a 116-run stand with Dhoni.
But he finally perished to Trent Boult going for one more big hit as India bowed out in stunning style.
New Zealand lean on Williamson, Taylor
Kane Williamson walked into bat when New Zealand were 1-1 after 3.3 overs with the Indian fast bowlers making the ball swing and seam in overcast conditions.
But the ice-cool Williamson played a couple of singles to settle down and punched Bhuvneshwar Kumar straight down the ground for just the second boundary of innings.
He ploughed his way through with his old-school batting, alongside Henry Nicholls, as the right and left-handed combination kept the scoreboard ticking on a tough pitch for batting.
It has largely been New Zealand's story in this World Cup with Williamson often left picking up the pieces and building the innings.
Middle-order batsman Ross Taylor has been Williamson's partner on several occasions and once again put up his hand up to deliver.
He put on 65 runs with Williamson for the third wicket and then took on the challenge alone, eventually top-scoring with 74 after the skipper's departure for 67.
Those runs proved priceless as New Zealand's bowlers took over with a scintillating display that caught India completely off-guard.
'One bad day'
Virat Kohli admitted India had paid the price for "45 minutes of bad cricket" as the heart-broken skipper surveyed the wreckage of exit.
"We've played outstanding cricket throughout this tournament. To just go out on the basis of 45 minutes of bad cricket is saddening," Kohli told reporters.
"It breaks your heart also, because you worked so hard throughout the tournament to build momentum, you finish number one in the table, and then a spell of bad cricket and you're out of the tournament.
"New Zealand deserves a lot of credit because they really put up a great display of how to bowl with the new ball. They hit perfect line and length and forced us to make errors."
'Brilliant fighting effort' by New Zealand
Kane Williamson praised New Zealand's "brilliant fighting effort" as his side reached their second successive World Cup final.
"A brilliant fighting effort from our guys on another tough surface," Black Caps skipper Williamson said.
"We wanted 240, 250. Then to have the start with the ball we had was an outstanding way to kick things off and get us into a position of strength."
Reserve day saved the match
Thanks to the reserve day scheduled for both the semi-final and final, fans were able to watch the full 50-over match.
New Zealand scored 139 for a loss of eight wickets in a rain-hit match that which was forced into the reserve day.
Resuming on the reserve day at 211-5, New Zealand added 28 runs from the remaining 23 deliveries.
On the second day, there were no rains interruptions and a 50-over match was completed.