De Villiers top-scored on 72 not out, with du Plessis making 67 and Wayne Parnell contributing 29 off 12 balls before he was run out.
The Proteas lead the five-match series 2-1 and can wrap it up if their attack can exploit the wicket at Hamilton's Seddon Park.
New Zealand's bowlers failed to make the most of the spin-friendly pitch, bleeding 72 runs off the final five overs.
While South Africa suffered a mid-innings wobble, de Villiers and Parnell's late 63-run partnership saw them finish strongly.
The Black Caps' decision to play an extra spinner in Jeetan Patel paid early dividends when Quinton de Kock went for a golden duck in the opening over.
De Kock, who had scored half-centuries in his previous five ODIs, misread the flight of a sharply turning delivery and edged the ball to the keeper.
Hashim Amla (40) took up the aggressor's role, smashing 14 off one Trent Boult over, but became Patel's second victim when he paddled the ball onto his stumps.
Du Plessis took a more conservative approach and was rewarded with his 25th ODI half-century off 97 balls.
He and JP Duminy guided the Proteas to 122 for two at the halfway mark, but Duminy's departure for 25 heralded a mini-collapse.
Du Plessis and David Miller followed in rapid succession, then Dwaine Pretorius was run out after de Villiers called for an ambitious single.
With South Africa looking shaky at 158 for six, de Villiers worked with Chris Morris (28) and Parnell to carve out a challenging target.
De Villiers' innings, the 52nd ODI half-century of his career, featured three sixes and four fours.
New Zealand's batting line-up has been bolstered by the return of opener Martin Guptill and the inclusion of wicketkeeper Luke Ronchi to replace Tom Latham.
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