The White Ferns posted a competitive total of 225 for seven off their 50 overs with opener Suzie Bates hitting 82 before becoming one-day international debutant Charlotte Russell’s first victim.
Bates hit seven fours in her 100-ball innings and was well backed up by 34 from Sara McGlashan and 28 from Nicola Browne - both of whom fell foul of Gunn.
Holly Colvin chipped in with 3-36, ripping out the Kiwi middle-order, including captain Haidee Tiffin, stumped by Jane Smit for 23.
But a late flurry from numbers eight and nine, Sarah Tsukigawa (21 off 25 balls) and Helen Watson (20 off 14) proved to be the difference between the two sides as England were bowled out for just 204 with seven balls remaining.
Gunn was sent in to open the innings and relished the chance she was given, finding the gaps and pushing for quick singles, as well as finding the boundary seven times.
She was eventually caught and bowled by player-of-the-match Bates who added figures of 3-20 and two catches to her batting heroics.
With four of the top six England batsmen falling to run-outs, New Zealand’s fielding was exemplary and kept them in the hunt from the early stages of the innings.
Caroline Atkins’ 32 gave England a sniff of getting up to the visitors’ total, but when she was out with the score on 178, the lower order capitulated, with Bates having a hand in all of the last four wickets.