Herschelle Gibbs made 119 off 101 balls as South Africa chased down New Zealand's 238 for eight with 28 balls to spare in the third and final one-day international at Newlands.
Victory gave the Proteas a 2-1 win in the series.
Gibbs crashed 10 fours and seven sixes in a sparkling innings, sharing an opening partnership of 173 with captain Graeme Smith. When he reached his century the total was 136 and Smith was on 29.
Playing on his home ground, Gibbs raced to fifty off 40 balls and reached his 19th one-day international century off 77 deliveries.
Smith battled his way to 51, surviving chances on 23 and 44 before he was caught at deep midwicket off spinner Daniel Vettori for 51.
That prompted a mini-slump as Gibbs went four overs later, then AB de Villiers and JP Duminy in quick succession as four wickets fell for 18 runs.
Jacques Kallis and Mark Boucher steadied the South African ship, putting on 46 and getting to within two runs of the win, before Kallis chased a wide ball and was caught behind off part-time bowler Lou Vincent.
Earlier, New Zealand had struggled after winning the toss.
The Kiwis were reduced to 79 for four after fast bowler Dale Steyn, playing in his first match of the series, dismissed both opening batsmen cheaply.
Scott Styris (60) and Mathew Sinclair (73) put on 49 for the fifth wicket and Sinclair then shared stands of 56 with Oram and 43 with Kyle Mills, as the Black Caps reached what looked a competitive total. Gibbs had other ideas.