The hosts ended on 192 for four after England had posted 194 for seven courtesy of a 93-run partnership between captain Eoin Morgan, who finished 80 not out, and Dawid Malan (53).
Despite advancing to the final, Kane Williamson's side should have won the game comfortably after Colin Munro (57) and Martin Guptill (62) blasted an impressive 78-run opening partnership in 6.3 overs.
The 30-year-old Munro smashed an 18-ball half century, which included seven sixes, before England's spinners Adil Rashid, who dismissed Munro on his third delivery, and Liam Dawson choked off New Zealand's scoring.
Guptill and Mark Chapman, however, saw off the threat of the two main spinners to add 64 runs in 5.2 overs and ensured New Zealand were within sight of the final before Guptill was bowled by Malan with his side 164 for three.
Chapman, who was bowled by Chris Jordan in the penultimate over for 32 but then recalled as the bowler had overstepped, and Colin de Grandhomme, however, were unable to score the 12 runs needed from the final over from Tom Curran.
Morgan, who had missed England's last two games in the series due to a groin strain, proved he had not lost any form while sitting on the sidelines with a composed innings.
The lefthander was on 37 when Malan departed with the score on 117 for three and then scored 40 of his side's next 48 runs but was starved of the strike in the final two overs.
Australia won all four of their games and are favourites for Wednesday's final at Eden Park in Auckland.
(Reporting by Greg Stutchbury in Wellington; Editing by Amlan Chakraborty)
