Taylor, by his own admission, was scratchy for some time before getting going for his fifth century, while Williamson's blazing unbeaten 100 from just 69 balls, secured with a sprawling third run off the last ball of the innings, was a cracking contribution.
The pair hurtled along near the end, 96 coming from the last seven overs to complete a 95-run stand in 22 overs.
But then it all went wrong, from New Zealand's point of view.
The bowling was uniformly ordinary on a good pitch and fast outfield.
This wasn't a case of Zimbabwe coming home on a wet sail in the final overs. Indeed, they were far ahead of New Zealand on comparative run rates with 15 overs remaining, before wobbling in the closing stages.
Brendon Taylor made 75 to follow two centuries in the earlier games; Tatenda Taibu made a tidy 39-ball 53 before Malcolm Waller and Elton Chigumbura added 112 from only 85 balls. All New Zealand's were hit; none seemed to have any idea about where to bowl consistently, which is a fairly important part of the deal. Some of the bowling was simply awful.
No Tim Southee, no Kyle Mills, no Daniel Vettori. This looked a seriously thin attack and Zimbabwe, with nothing to lose, had a crack at them.
Waller got Zimbabwe home with one ball to spare, finishing unbeaten on a 74-ball 99. He, with Chigumbura, Taibu and Taylor, struck some superb, clean shots interspersed with cross-bat heaves and it was their day.
Chigumbura deserved rather better than an undignified sendoff from Jacob Oram too, but New Zealand would still have won had the skipper not grassed Waller three times.
A regulation edge to fourth slip went down on 46, and Taylor twice put Waller down in the final over, one far harder than the other.
It was Zimbabwe's first win over New Zealand since January 2001 at Eden Park, and their eighth overall from 32 games.
In the previous two games they had had some decent moments without ever looking likely to press on and complete the job.
"At this ground it's always hard to defend a score so we knew we had a chance of chasing it down as long as we batted well," Chigumbura said.
Ross Taylor said the core of the series had been the old axiom that "if you drop catches you lose a match". He discovered that personally yesterday.
New Zealand have a two-day match starting in Bulawayo on Saturday.
BY THE NUMBERS
* The 195-run fifth wicket stand by Ross Taylor and Kane Williamson is a New Zealand record against all nations.
* It is the first time New Zealand have lost an ODI after two of its batsmen had scored centuries.
* It is the second time New Zealand have lost an ODI after scoring more than 300 batting first, India having chased down 315 for seven in Bangalore last December.
* This was Zimbabwe's biggest successful run chase, far exceeding the previous 290 for four against the West Indies 11 years ago.
* The 657 run-aggregate was the highest for any ODI in Zimbabwe.