New Zealand began the last day on 230 for six, requiring another 128 runs to win, with Ross Taylor not out on 79.
South Africa A took control of the match when fast bowler Friedel de Wet, who took six for 50 in the first innings, had Taylor caught spectacularly for 86 by a diving Boeta Dippenaar in the fifth over of the day.
The same combination accounted for Shane Bond for six and the introduction of spin then saw off-spinner JP Duminy bowl Iain O'Brien for six.
Gulam Bodi delivered a left-arm googly to dismiss Daniel Vettori for 30 and signal the end of the match.
De Wet, who finished with three for 76 in 23 overs, and left-armer Lonwabo Tsotsobe (three for 53) were the pick of the home side's bowlers.