Taylor required two runs off the final ball of the Black Caps' innings before he knocked Wayne Parnell's ball for four to finish 102 not out.
Taylor and Jimmy Neesham put on an unbroken record stand against South Africa for the fifth wicket, 123 overtaking the old mark of Adam Parore and Shane Thomson at Centurion in 1994-95. De Kock went about business in the only way that he's familiar with and attacked the bowling with Faf du Plessis for company.
Captain Kane Williamson and Taylor stabilised the innings with a 104-run partnership, during which Williamson breezed past his fifty, before he was sent packing by Imran Tahir for 69, which came off 75 balls and included six boundaries.
Taylor, who also posted a century in that match, needs Test tons against two more teams (South Africa and Bangladesh) to join Williamson in that club, which now has 13 members.
New Zealand named an unchanged lineup and finds itself under pressure to quickly recover from the first match loss which handed South Africa a 1-0 lead in the five-match series.
Even though Neil Broom (2) fell cheaply, Taylor along with James Neesham (71 not out) ensured New Zealand reached 289 for four in the 50 overs with their unbeaten 133-run stand.
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Taylor had shared the New Zealand record of 16 ODI centuries with Nathan Astle, and had been in a rich vein of form since returning from eye surgery in early January.
Quinton de Kock and captain AB de Villiers steadied for South Africa as they looked to ramp up the scoring to match the run-rate needed.
Taylor was awarded the man of the match for his brilliant century as New Zealand levelled the series 1-1.
Boult then had de Villiers caught behind by Tom Latham for 45 before Chris Morris was brilliantly run out with a backhand flip by Dean Brownlie.
The target was down to 20 runs off the final two overs and Boult castled the South African all-rounder in the final ball of the penultimate over leaving 15 runs to get off the final six deliveries.