Gunn and Guha displayed a fine spell of seam bowling to bundle out White Ferns for paltry 72 in 30 overs.
NZ skipper Haidee Tiffin won the toss and chose to bat but her decision backfired as only herself and Rowan Milburn reached double figures in a below-par performance.
Aimee Mason, who scored century in the previous tie to help tourists clinch the series 3-0, was rested for this clash.
Gunn took 4 for 27 in her nine overs but it was the highly economical figures of the recalled Guha with 4 for 11 from 7.5 overs that proved to be decisive in England's first victory of the campaign.
In reply the hosts struggled against Browne but they reached the target with opener Sarah Taylor coming good once again with an unbeaten 49.
Nicola Browne took three wickets for the White Ferns.
England made two changes to their team with Guha and off-spinner Charlotte Russell coming in for Laura Marsh and Lynsey Askew.
New Zealand 72 all out in 30.5 overs (Milburn 15, Tiffen 13; Guha 4 for 11, Gunn 4 for 27) lost to England 73 for 4 in 27.3 overs ( Sarah Taylor 49 n o; Nicola Browne 3 for 25)