The tourists appeared sure to prevail in Dunedin when Jonny Bairstow’s wonderfully clean striking and Joe Root’s perfect foil took them to 267-1 with twin hundreds in an all-Yorkshire stand of 190.
But once Bairstow went for 138, an alarming collapse of six wickets for 21 runs took hold largely to the leg-spin of Ish Sodhi (4-58) as England had to settle for 335-9.
Then Taylor (181no), who came to the crease at 2-2 and suffered increasingly with the quadriceps injury which ruled him out of the previous match, launched a telling recovery with captain Kane Williamson and Tom Latham (71) to secure victory with three balls to spare and set up a series decider in Christchurch on Saturday.
Bairstow’s departure, after hitting seven sixes and 14 fours from 106 balls, kick-started England’s crumble when a huge total was there for the taking.
Their innings was an oddity of extremes, reaching an imperious position yet then contriving a remarkable misfire before No 10 Tom Curran hit four of the last five balls from Tim Southee for four.
Bairstow and Jason Roy hit the accelerator from the outset after being put in on a pitch which spent almost the entirety of the previous day under cover from hours of rain.
The opening stand of 77 took under 11 overs until Roy mis-swept Sodhi’s second delivery low to Mitchell Santner at short fine-leg.
But Santner was culpable when he put down an easier chance at extra-cover off Trent Boult to reprieve Bairstow on 74.
The Yorkshireman continued to clear the ropes at apparent will - and Jos Buttler’s national-record eight sixes in an ODI innings was at his mercy, as was Roy’s highest individual score of 180, until Bairstow skewed another attempted big hit for a steepling catch at short third-man off Colin Munro.
It was a moment which appeared to spell little more than brief respite for New Zealand, especially when Eoin Morgan promoted Buttler to No 4.
But the first of England’s middle-order hitters poked a low return catch back to Sodhi to go for a second-ball duck, and the potential might of Morgan, Ben Stokes and Moeen Ali quickly amounted to a mere nine runs.
Root looked incredulous at the other end, forced into accumulation as 50 balls passed between the 40th and 48th over without a single boundary.
He stuck at it, completing his 11th ODI hundred from 95 balls, before he was caught behind trying to pull Southee.
Within three overs of the chase Munro was lbw for a golden duck, needlessly taking New Zealand’s review back to the pavilion with him, after Mark Wood pinned him in front of middle - and both openers were gone without a run between them when Martin Guptill tried to hit Chris Woakes over the top but holed out to mid-off.
Stokes’s first delivery was then too much for Williamson, caught down the leg-side and unable to review despite his apparent disappointment with the decision.
But more significantly, Moeen dropped a straightforward caught-and-bowled offered by Latham on four, and gradually it emerged there would be no way back for England during a stand of 187.
There were two late wickets for Curran, but Colin de Grandhomme’s big hitting applied most of the finishing touches before Henry Nicholls settled matters with a winning six in the final over.
Taylor remained unbeaten with 17 fours and six sixes from 147 balls after passing his career-best on the eve of his 34th birthday.