Needing 154 runs to book their tickets for Sunday’s title clash, England overhauled the target in 17.1 overs.
Opener Jason Roy played a starring role with the bat for England, plundering 78 runs off 44 balls. The 25-year-old right-hander hit 11 boundaries and a couple of sixes during his innings.
England, who won the World T20 in 2010, are thus in line for their second title in the shortest format of the game.
In the final, they will meet the winner of the second semi-final between India and West Indies which will be played in Mumbai on Thursday.
New Zealand were the only unbeaten team in the group stage and were expected to put up a strong fight. But England were far superior with both bat and ball on a pitch which was not too easy to bat on.
The former winners were boosted by a quick opening partnership of 82 runs in 50 deliveries between Roy and Alex Hales (20). Hales departed when he mistimed a Mitchell Santner delivery into the hands of Colin Munro at long-on, but the early momentum kept England in good stead.
Leg-spinner Inderbir Singh Sodhi gave the Kiwi fans a glimmer of hope by sending back Roy and England captain Eoin Morgan off consecutive deliveries in the 13th over. But that did not prove to be enough to carry New Zealand through.
Jos Buttler brought up the winning runs and underlined England’s dominance in spectacular fashion by pulling a Santner delivery into the stands beyond the midwicket fence.
Sodhi registered figures of 4/42 in his four overs, while Santner (1/28) was the only other New Zealand bowler to claim a wicket.
Earlier, asked to bat first, New Zealand posted a competitive total of 153/8 in their 20 overs.
The Kiwis should have got a bigger total, but England did well to take wickets regularly in the latter half of the innings to restrict their opponents.
Munro put in a useful knock for New Zealand with the bat, scoring 46 runs off 32 balls with seven boundaries and a six.
Experienced pacer Ben Stokes was the most successful among the England bowlers with figures of 3/26. Talented left-arm pacer David Willey (1/17), Chris Jordan (1/24) and off-spinner Moeen Ali (1/10) got a wicket each.
Liam Plunkett endured severe punishment in his first spell, giving away 21 runs in just two overs, before finishing his four overs with figures of 1/38.
Willey handed England an early breakthrough as Martin Guptill lashed out at one that shaped away only to see the edge carry to Jos Buttler behind the stumps.
Munro and Kane Williamson proceeded to lay the foundation for a competitive total with a 74-run partnership in 50 balls.
Munro was in superb form, smashing the England bowlers to the ropes with monotonous regularity. He was especially harsh on Liam Plunkett, hitting the pacer for three consecutive boundaries in the sixth over.
Williamson perished through an easy caught and bowled effort by Ali after tossing a skier to mid-off. Plunkett had his revenge on Munro in his second spell when the Kiwi left-hander went after a delivery which was well outside off, only to slice it to Ali at third man.
That seemed to slow down the New Zealand run rate a bit. Ross Taylor did not last long, snapped up by Eoin Morgan off Chris Jordan’s bowling in the 17th over.
Anderson seemed to be in good knick, scoring 28 off 22 deliveries. But his dismissal in the 18th over ened Kiwi hopes of amassing a big total.
New Zealand 153/7 (Colin Munro 46; Ben Stokes 3/26) vs England 159/3 in 17.1 overs (Jason Roy 78, Jos Buttler 32 n.o.; Inderbir Singh Sodhi 2/42).