Taylor completed his ton in dramatic fashion with a boundary off the last ball of the innings to finish 102 not out and claim a New Zealand record of 17 ODI centuries.
The 32-year-old, who had shared the record of 16 with Nathan Astle, received solid support from captain Kane Williamson and all-rounder Jimmy Neesham.
Neesham scored an unbeaten 71, while Williamson notched 69 -- a return to form for a batting line-up which has been over-reliant on tail-end contributions recently.
Latham, in particular, will face intense pressure to keep his place after ducks in his previous two ODIs.
Dwaine Pretorius was the best of the South African bowlers, taking two wickets.
South Africa's captain AB de Villiers gave the Proteas a huge injury scare in the sixth over when he collapsed to the ground writhing in pain after landing heavily on his shoulder while fielding.
But de Villiers, who returned from elbow surgery last month, stayed on after consultations with team physiotherapist Brandon Jackson.
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