The touring side secured the triumph courtesy of a commanding 65-run victory in Monday's second T20, after the first match was abandoned following the completion of one innings.
Thursday's decider in New Zealand lasted 3.4 overs before the covers were deployed with the hosts on 38-1 after being put into bat.
Opener Tim Seifert had smashed 23 runs from 11 deliveries, while Tim Robinson fell victim to Brydon Carse, caught in the deep.
"Very frustrating. The weather hasn't been ideal but good to get a little bit of game time out there," said England captain Harry Brook, who was also named the player of the series after scoring 98 runs.
"It's a great place to tour, we've had a great time so far and we're looking forward to the ODI series. We've had an amazing time.
"There will be a few changes in the side (for the ODI series), a few big names come back and hopefully we can keep that momentum going forward."
The three-match ODI series begins on Sunday.
"This time of the year, it's always a potential but some good things to come out of the series, it's always nice to play England," New Zealand captain Mitchell Santner said.
"The way we bowled in the first game. The second game was good, we were put under a lot of pressure on a good wicket and you take learnings from that.
"We're trying to fine tune what we've got before the T20 World Cup (next year)."