Cook’s tourists looked on target for an opening victory at Seddon Park until Martin Guptill and captain Brendon McCullum (69no) sparked a revival for the Kiwis.
Individual half-centuries from Ian Bell (64), Jonathan Trott (68) and Joe Root (56) set England on the right track but bowler Mitchell McClenaghan — who dropped out of his final over with a series-ending side strain — finished with four for 56 as England ran out of steam on 258 all out.
Guptill led the hosts over the line with 24 runs from just 10 balls and Cook said: “He’s obviously a very dangerous player.
“Whether he bats at the top of the order or coming in there at six, he’s very hard to bowl to.
“The trick is to try to get him out early.”
Despite the loss, it was a notable day for James Anderson, who made England cricket history by taking his 529th international wicket — the most by any Englishman.