Spinners Graeme Cremer and John Nyumbu shared five wickets as Zimbabwe kept New Zealand to 273 for six in Friday`s decisive third one-day international at Harare Sports Club.
With Kane Williamson recording his sixth straight score of 50 or more, New Zealand appeared set for a dominant total, but Cremer and Nyumbu struck at crucial times to set up an intriguing run chase.
Preferred to Prosper Utseya because of his more attacking style, offspinner Nyumbu made the initial breakthrough when he dismissed Tuesday`s centurion Tom Latham.
New Zealand rebuilt to reach 100 for one in the 21st over, but Cremer`s double-strike kept them in check as he had Martin Guptill caught at slip for 42 and then spun one through the defences of Colin Munro.
Williamson and Grant Elliott added 70 for the fourth wicket to set up a big push in the final 10 overs, only to be thwarted when Elliott top-edged a Cremer delivery to short fine leg to depart for 36, and Williamson was brilliantly caught on the boundary by a juggling Craig Ervine.
The New Zealand captain fell for 90 -- the fifth time this year that he has been out between 90 and 100.
It took an unbroken stand of 50 in just 25 balls to give New Zealand the late boost they required, as James Neesham finished unbeaten on 37 and Nathan McCullum struck 25 not out from 16 deliveries.
The tourists were without key batsman Ross Taylor, who was ruled out of the remainder of their tour of Zimbabwe and South Africa when he suffered a blow to the groin in training on Thursday and required minor surgery.