In a see-sawing match, the Proteas initially blunted the Black Caps attack then endured a late batting collapse that restricted them to 282-9 before skittling the home team for 210 with 21 balls to spare.
The win gives the tourists an unassailable 2-0 lead in the three-match series and AB de Villiers' men could snatch the world number one ODI ranking from Australia if they complete a 3-0 whitewash in Hamilton on Monday.
The Proteas then lost six wickets for 25 runs in the dying stages of the innings, including four in the last three overs.
But by then the damage was done and South Africa had a target that left New Zealand's weakened batting line-up little chance with wicketkeeper Luke Ronchi's 79 the highlight for the Black Caps.
"It was a bit frustrating at the end... It turned out to be a long innings for us bowling-wise but the first 35-40 overs I can't fault," de Villiers said after his attack eased up with New Zealand on the ropes and victory in sight.
"It wasn't great, there was a real lack of craft again with the bat," skipper Brendon McCullum said. "We showed a little bit of backbone at the end but far too little too late."
The Black Caps boosted their fast-bowling stocks with the addition of a fit-again Tim Southee and Mitchell McClenaghan, but it began as a frustrating day for the pacemen.
Amla was let off the hook when he edged Southee on five, only for wicketkeeper Ronchi and Tom Latham in the slips to let an easily catchable chance sail between them to the boundary.
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