They removed India's top-order batters in no time to have them at five for three and then at 24 for four.
For the first time in global history, a team lost its first three batsmen all for 1 as India saw Sharma, Kohli then Rahul depart in the space of 10 balls and was marooned on 5-3 after 3.1 overs.
The opening semi-final of the Cricket World Cup was restarted on the second day after rain prevented the match finishing as scheduled on Tuesday.
New Zealand will play England or Australia in the final at Lord's on Sunday.
Needing 240 to win, India would have been the first side to successfully chase down a target at Old Trafford in this tournament, and pretty much everyone would have expected them to do so. "We will consider that selection if we have to", Williamson added.
Given how India were touted as favourites, just like they were coming into their match against New Zealand, Boult admitted that the Black Caps were inspired by the way in which Pakistan defeated India. The ball was just clipping the bails and he was given out by the on-field umpire.
The Kiwis had lost their last three games in the group stage, which was topped by India, who themselves suffered only one defeat.
Two balls later, Dhoni had run himself out, thanks to a brilliant direct hit by Martin Guptill. Soon after Jadeja returned to pavillion after playing a scintillating knock of 77 runs in 59 balls, Dhoni made a decision to take control of the Indian run-chase as he despatched Lockie Ferguson for a six.
James Neesham took the final wicket of Yuzvendra Chahal as India were bowled out, with the Kiwis claiming a dramatic victory.
First Rohit Sharma, who needed 27 to set a new tournament record for most runs in a single World Cup campaign, overtaking compatriot Sachin Tendulkar who amassed 673 in the 2003 edition, was caught behind.