Taylor, 32, registered his 17th ODI century with an unbeaten 102 as New Zealand posted 289-4.
Record-breaking Ross Taylor guides New Zealand to six-run victory, which levels up the five-match one-day series against South Africa.
Choosing to bowl first, South Africa struck early as Wayne Parnell dismissed New Zealand opener Tom Latham for just two runs.
After adding 40 runs with skipper Kane Williamson (69), Brownlie was trapped LBW by Dwaine Pretorius (2-40) in the 13th over. Mitchell Santner, however, had him stumped when on 34 as one wicket brought another for the hosts with de Kock departing two overs later for 57.
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South Africa, who won the opening match at the weekend with a ball to spare, were given a platform in their response by Quinton de Kock's 57 at the top of the order, but, despite the rest of the top six getting into double figures, none of them could go on to make a big score.
The only other change to the Proteas line-up sees batsman David Miller replace Kagiso Rabada, who de Villiers said had a knee niggle. His knock of 50 off 27 balls comprised of two sixes and four boundaries in a stand with Andile Phehlukwayo (29) who had proven his skills with the bat even in the first match. Jimmy Neesham provided the fireworks for the home crowd with his 71 not out (57 balls, 6 fours).
Taylor's century came in the final ball of the innings when he smashed a boundary to go past Nathan Astle's record of 16 while Neesham scored at a strike-rate close to 125. That said, South Africa's bowlers pulled things back well, despite conceding over seven in that partnership, not letting the pair let loose after the foundation that they had laid.
Soon after he scored his 11th half-century, de Kock holed out to deep square to give Boult (3-63) his first wicket and South Africa slipped to 124 for four.
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