South Africa celebrate the wicket of Martin Guptill of New Zealand ( R) during the third and final One Day International (ODI) cricket match between South Africa and New Zealand at the Kingsmead cricket ground in Durban on August 26, 2015. PHOTO: AFP
The win enabled South Africa to leapfrog New Zealand into third place in the world one-day rankings, behind Australia and India.
It also provided a measure of revenge for their heartbreaking defeat to the Kiwis in the World Cup semi-final earlier this year.
De Villiers hit his runs off 48 balls to enable South Africa to reach 283 for seven on a pitch which offered some assistance to the seam bowlers throughout the match.
New Zealand were bowled out for 221 in reply.
New Zealand lost key batsman Martin Guptill early, caught behind off Dale Steyn, but a partnership of 84 off 118 balls between Tom Latham and captain Kane Williamson kept them in contention.
Both batsmen, however, were dismissed in the space of 15 deliveries.
Williamson was bowled for 39 when he charged down the pitch and missed a straight ball from leg-spinner Imran Tahir.
Latham completed his third successive half-century but was run out for 54 by a direct hit from backward square leg by David Miller.
With the required run rate climbing, New Zealand lost wickets at regular intervals. Medium-pacer David Wiese took three for 58.
"The first two games were roller-coaster rides but we showed our commitment and resilience tonight," said De Villiers.
"We had to work hard to get our runs and all the bowlers did really well."
Williamson said his team's bowling effort had been 'steady'.
"The batting never gained momentum and we never got ahead of the game at any stage."
New Zealand were missing several of their leading players during the tour, which also encompassed one-day and Twenty20 series in Zimbabwe.
"Overall this tour has been of great benefit," said Williamson.
"A bunch of individuals got a lot out of it."
De Villiers, who hurried to a half-century off 38 balls, hit eight fours and a six.
When he was on 19 he reached 8000 runs in one-day internationals in his 182nd innings - the fastest to the milestone.
The previous record was held by Sourav Ganguly of India, who took 200 innings.
After a poor batting performance in the second match in Potchefstroom, where they were bowled out for 204, South Africa fulfilled their objective of making a solid start as Morne van Wyk (58) and Hashim Amla (44) put on 89 for the first wicket.
But the scoring rate was languishing until De Villiers and David Miller (36) put on 86 off 65 balls for the fourth wicket.
Farhaan Behardien kept the scoreboard moving, hitting 40 off 28 balls before he was caught off the last ball of the innings.
Left-arm opening bowler Ben Wheeler took three for 71 but medium-pacer Grant Elliott was the pick of the New Zealand bowlers, taking two for 41 in an unbroken ten-over spell.
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