The Black Caps needed 57 off 24 balls and won with an over to spare, with Jimmy Neesham exploding with 27 from 11 balls, before Player of the Match Daryl Mitchell finished the job, with his unbeaten 72 from 47 deliveries.
Chris Jordan surrendered 23 runs off the 17th over, getting New Zealand back in the game, with 14 coming from Adil Rashid’s next, but also Neesham’s wicket.
Needing 20 from 12, Mitchell hit two sixes from Chris Woakes, before clinching victory with a boundary off the final ball of the over, confirming New Zealand’s maiden appearance in a T20 World Cup final.
“We went through our plans but sometimes you have to take your hat off to certain people. Today just wasn’t our day,” Silverwood added.
New Zealand skipper Kane Williamson, who was dismissed early as the Black Caps slumped to 13-2 in pursuit of England’s 166-4, praised Mitchell and Neesham.
“Outstanding from Mitchell at the top, but cashing in on the match-ups (was crucial),” he said. “His character stood out today, an incredible knock, not done it a lot at the top of the order.
“T20 cricket is a game of small margins, depending on the surface, short side can all be match-defining. We had wickets in hand which was really important.
“Neesham came out and hit the ball hard, and changed the momentum of the game. Ultimately the deciding factor.”