Wayne Parnell struck twice in the powerplay before the South African spin duo of Keshav Maharaj (3-17) and Tabrazi Shamsi (2-6) ran through New Zealand's batting line up.
South Africa finished their engagements with five points from as many games.
South Africa's pace duo Anrich Nortje and Sisanda Magala have been ruled out of the World Cup because of injuries, Cricket South Africa confirmed on Thursday.
India opener Shubman Gill's reign at the top of the ODI batters' list was short-lived as he was replaced by former Pakistani skipper Babar Azam in the ICC Player Rankings issued on Wednesday.
India's solitary ODI series win in the Rainbow nation occurred in 2018, emphasising the need for a strong beginning from Ruturaj Gaikwad and B Sai Sudharsan.
Indian team will certainly feel a sense of deja vu when it takes on a red-hot South Africa on Sunday in what will be a battle of equals
IMAGES from the T20 World Cup FINAL played between India and South Africa in Barbados on Saturday
Star batter Virat Kohli, who is the second leading run-getter in the World Cup with 354 runs after five matches, has improved three spots to be on joint fifth spot with Aussie left-handed opener David Warner (up two spots).
Chasing targets has been their Achilles heel throughout the tournament. The same batters who've plundered the bowling and scored daddy hundreds batting first, have resembled pale shadows of themselves chasing targets.
The most interesting aspect of the contest is the form of batters from both sides which has been the reason of their success so far.
Will Rohit Sharma get one final opportunity to salvage his Test career?
Rohit Sharma jumped five places to sixth in the ICC ODI ranking for batters.
Pakistan needs to win all its matches and expect Australia to falter in at least two of their remaining four games.
RR could not have asked for a better start to the season, registering four consecutive wins from as many games.
South Africa dug deep to deny Australia a 3-0 series sweep with a battling draw in the rain-disrupted third Test at the Sydney Cricket Ground on Sunday, finally finding some fight on the final day of a miserable tour.
Kohli has elevated one spot to secure the third position in the latest ODI Player Rankings
South Africa skipper Aiden Markram applauded his bowlers for sealing a thrilling seven-run victory over England in a T20 World Cup Super Eight Group 2 match in St Lucia on Friday, saying they did not wilt under pressure.
South Africa's batting innings was also boosted by a superb 56 from 27 balls from Aiden Markram as he struck five sixes on the small County Ground, while new find Tristan Stubbs blasted a breezy 24 off 11.
In need of a victory to firm-up their position in the IPL play-offs race, Chennai Super Kings have the heavy task of nullifying a deeply hurt and frustrated Rajasthan Royals in Chennai on Sunday.
IMAGES from the IPL match between Punjab Kings and Rajasthan Royals played in Mullanpur on Saturday
There will be plenty of scrutiny of the Newlands pitch with the match completed in 642 balls, the shortest ever test in which there has been a winner, beating Australia's 656-ball victory over South Africa in 1932.
Meanwhile, South Africa have included uncapped off-spinner Prenelan Subrayen and seamer Lizaad Williams in their squad for the two-Test series in the West Indies that starts on June 10.
Rishabh Pant hailed the fighting spirit of the side after the hosts came back from two games down to take the five-match series against South Africa
India, missing their top players, aim to punch above their weight and seal a memorable series victory against South Africa in the third and final ODI in New Delhi on Tuesday.
Images from the ICC World Cup match between Afghanistan vs South Africa, in Ahmedabad, on Friday.
The board said no replacement will be brought in for Rabada as there is an extended squad in place in the Bio-Secure Environment (BSE), but George Linde has been retained from the Test team as an extra spin-bowling option for the series.
South Africa have recalled top-order batsmen Faf du Plessis and Rassie van der Dussen for their three-match One-Day International tour of India later this month, while left-arm spinner George Linde is named in the squad for the first time. The squad will be captained by Quinton de Kock and play the first ODI in Dharamsala in March 12.
England will need to defeat Namibia in their last league match and hope that Scotland lose to Australia.
Rohit Sharma completed a century in each innings in his maiden Test as opener as India pressed for victory in the first Test against South Africa by setting the touring side a daunting target of 395.
Left-arm spinner Maharaj (3/189 in 55 overs) bowled his heart out but did not get the support from the other end in Dane Piedt (107/1 in 19 overs) or debutant Senuran Muthusamy (63/1 in 15 lovers), who did take the prized wicket of Virat Kohli.
The Capitals have been inconsistent so far, winning five and losing six of their last 11 games.
The 34-year-old Steyn, currently on a short-term contract with Hampshire having been plagued by injury over the last two-and-a-half years, is three wickets short of a milestone that has frustratingly eluded him in recent times.
England will be looking to bounce back from a rain-affected opening match and solidify their T20 World Cup campaign
South Africa crushed Australia by 134 runs to cruise to their second victory at the World Cup, as Quinton de Kock struck back-to-back tons and Aiden Markram made a half-century before the bowlers ripped through the five-times champions on Thursday.
The bowling stocks looks good, but the major concern will be around the batting line-up, which struggled on the recent tour of England.
South Africa have an aching relationship with World Cup semi-finals, dating back to 1992. AB de Villiers had a close encounter with heartbreak in 2015. Now, he is hopeful that the current team will finally absolve his country of all the past pain.
A resurgent Mumbai Indians will need to address their bowling woes as they look to exact revenge on table-toppers Rajasthan Royals in their reverse fixture of the Indian Premier League in Jaipur on Monday.
'As a South African team, we know we're going to have that chip on our back, or that narrative that we have to get over'
Chasing an improbable target of 490 to level the series, the tourists finished day three on 139-5, their highest total in the spin-dominated series, at Colombo's Sinhalese Sports Club Ground.
Rossouw was supported by opener Quinton de Kock (68 off 43) while David Miller came in with four balls left in the innings to smash three sixes, guiding the tourists to a competitive total of 227.