Ravi Bopara failed to hit a six from the final ball, which would have sent the game into a super over, after New Zealand set a target of 201 for four - their highest total on foreign soil.
That meant England had to better their best ever chase - the 178 they managed against India in Mumbai last December - and were on course for the majority on a fast-paced surface. But their pursuit faltered on the back of some inspired captaincy from Brendon McCullum, who earlier joined Hamish Rutherford (62) in a blistering 114-run stand.
With England 134 for two in the 14th over McCullum rolled the dice and left in a slip for Eoin Morgan. The stand-in England skipper obliged by slashing a chance that Ross Taylor brilliantly held on to before Luke Wright edged behind in the next over for a 34-ball 52.
Bopara (30 not out) and Jos Buttler - two of the players retained from Sunday's Champions Trophy defeat to India - edged them close but they ended up losing by the same margin again.
Morgan led the side in the absence of Stuart Broad and his fellow Irishman Boyd Rankin, the 6ft 7in quick, was handed his England debut. While he took four balls to snare his first wicket for his adopted country, Rutherford and McCullum took charge thereafter to make Morgan's decision to send them in appear the wrong one.
England got off to the flying start they required in pursuit as openers Alex Hales (39) and Michael Lumb crashed 50 from the first 28 balls. Lumb (29) brought up the landmark with a straight six off Nathan McCullum, but unluckily jammed the next ball into his pads and on to his stumps.
Hales mis-hit a Ronnie Hira full-toss down the throat of deep midwicket, but Wright loomed as the key man as he reached 50 off 29 balls. With New Zealand starting to need wickets Brendon McCullum bravely inserted a slip to Morgan and, when Wright followed, England suddenly needed 63 from the last five overs.
Bopara and Jos Buttler reduced the ask to 26 from the last two overs, which further decreased when Buttler scooped Butler for six to start the penultimate over. Buttler was then run out at the non-striker's end and 16 was needed from the final over from Corey Anderson. Ben Stokes hit the first ball for six, but when Bopara needed to repeat the dose at the end fell short.
Earlier, Rutherford had made an impressive 64 from just 35 balls and Brendon McCullum a powerful 68 from just 48 deliveries before Taylor chipped in with an unbeaten 32.