Haidee Tiffin won the toss for the visitors and chose to bat but her decision backfired as only herself and Rowan Milburn reached double figures in an under-par performance.
New Zealand took an unassailable 3-0 lead in the series on Sunday but were defeated by six wickets in the fifth match as opener Sarah Taylor continued her good form with an unbeaten 49.
Aimee Mason was rested for the clash after her hundred set up victory for the visitors in the previous game and she was badly missed by a New Zealand side who were completely outplayed by their England counterparts.
Gunn took 4-27 in her nine overs but it was the highly economical figures of the recalled Guha with 4-11 from 7.5 overs that proved to be decisive in England's first victory of the campaign.
Nicola Browne took three wickets for the White Ferns as England struggled initially, but they reached their target of 73 in 27.3 overs as Gunn provided the foil that Taylor needed after the middle order had capitulated.
England made two changes to their team with Guha and off-spinner Charlotte Russell coming in for Laura Marsh and Lynsey Askew.