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GB finished bottom of the Pool stage in London with no wins and only three goals scored, but produced their best performance in an enthralling fifth/sixth place play-off.
Alex Danson scored a match-winning hat-trick, with Lily Owsley also on target.
"We didn't lose belief and we are delighted," Danson told BBC Sport.
"Obviously I'm delighted [with the three goals] but not just for me, from a whole team perspective because we can build on that performance leading into the summer."
Head coach Danny Kerry admitted "harsh words" were spoken after Britain's 4-1 defeat by Australia on Saturday, but was please with how his team responded.
"We've had a tough tournament and they know that yesterday wasn't good enough, but today they really committed," he told BBC Sport.
Danson struck her first goal of the tournament in the 10th minute, but Anita McLaren drew New Zealand level in the second period.
Owsley and Danson struck either side of half-time to take GB clear, but back came the Kiwis with goals from Olivia Merry and Kelsey Smith made the score 3-3.
Danson needed time out after being struck in the head by the ball, but recovered to deliver a composed lofted finish over New Zealand keeper Sally Rutherford to win Britain the match.
"Although we conceded a few today, which we need to work on, overall that was much better," captain Kate Richardson-Walsh told BBC Sport.
"We have a lot to learn, huge amounts, but it's good we're doing that now and can take that forward to Rio."
British selectors will reveal the 16 women and 16 men who have been chosen to represent Team GB at this summer's Rio Olympics on Tuesday.

The newly minted millionaire was reported to have just returned from a holiday with his family when they were told the news.
"My husband was literally pumping the air when he was on the phone," said the unnamed child's mother, according to local media.
It is not known how the winner reacted.
Bonus Bonds are an investment that pays out thousands of prizes to savers, lottery-style, every month. NZ$1m is the biggest monthly prize.
The child's Bonus Bonds account was reportedly set up when he was born with just NZ$250 ($180; £140) worth of bonds, given by a relative.
ANZ bank, which runs the scheme, confirmed the win but said it was respecting the family's wishes by not giving further information about the winner.

Oxford City Council said the money had mostly been used for "ground investigations of possible sites" but nowhere suitable had been found.
Two cemeteries still have space, in Wolvercote and Botley, but they are expected to be full by 2018 and 2021.
The council said it had not given up and was "still exploring options".
Linda Smith, board member for leisure, parks and sport, said the council has been "searching for a suitable new burial site for many years".
She added: "But ultimately, as with new housing sites, we have run out of suitable land within Oxford.
"So far all the council-owned sites that we have identified have, following ground investigations and surveys, had to be discounted.
"Either due to the size of the site, the ground conditions, a high water table or a covenant restricting the use of the site."
After the two remaining cemeteries are full the council said only the reopening of family plots, the use of a few reserved plots, and the interment of ashes would be possible.
The last increase in burial space in Oxford was in 1932.
Britain's women beat New Zealand 4-3 to secure a first win at the 2016 Champions Trophy, in what was their final match before the Rio Olympics.
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A New Zealand toddler has won NZ$1m ($726,600; £560,700) in Bonus Bonds prize money - the youngest ever winner of the investment lottery scheme.
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A council has spent £30,500 unsuccessfully searching for new burial sites in Oxford over the last four years.