Du Plessis was initially given out on 27 when trapped in front by Jeetan Patel but had the decision overturned on review. He went on to finish unbeaten on 51 as the Proteas made 150-4 after bowling the hosts out for a paltry 149 in 41.1 overs.
David Miller produced a counter-attacking 45 not out to help the test captain ensure a 3-2 series victory, which vaulted South Africa back to the top of the one-day rankings.
New Zealand had threatened to make the run chase much more difficult than it should have been, reducing the visitors to 88-4 when they captured the important wicket of AB de Villiers for 23.
However, Du Plessis and Miller shook off some nervous moments with a 62-run partnership that lefthander Miller dominated.
"They put us under pressure and asked a few good questions," de Villiers said. "But a fantastic knock by Faf and David at the end to take us across the line.
"It was one of those totals that needed a bit of nit and grit and the two of them showed that."
New Zealand were never able to settle against a superb South African bowling attack, who created consistent pressure from both ends with numerous dot balls that was supported by strong work in the field.
Kagiso Rabada got South Africa going early by bowling Martin Guptill for four, ensuring there would be no repeat of the right hander's match-winning 180 not out in the fourth game in Hamilton on Wednesday.
Six New Zealand batsmen were dismissed for single figures, with Colin de Grandhomme top scoring with 32.
Rabada, who was generating good bounce off a length and troubled the batsmen as the ball hurried through, finished with 3-25 from 7.1 overs and was named man of the match.
Leg-spinner Imran Tahir, who conceded just 10 runs from his first seven overs, finished with 2-14 from his full complement.
"It was a disappointing effort with the bat," New Zealand captain Kane Williamson said. "We knew that if we put a score on the board we could scrap and put pressure on them.
"But credit to AB and South Africa for the series win. They outplayed us in this game."
The two sides now head to Dunedin for the first match of a three-test series, starting on Wednesday.
(Reporting by Greg Stutchbury in Wellington; Editing by John O'Brien/Peter Rutherford)
