The South Africans swiped 11 sixes, including five to Albie Morkel, to set up a 13-run win in the Super Eight match at Kensington Oval in Bridgetown, Barbados.
New Zealand were on track to haul in South Africa's 170 for four for periods of a creditable run chase but no batsman could establish themselves for long enough and they eventually settled for 157 for seven.
After winning two warmup games and their group matches against Sri Lanka and Zimbabwe in Guyana, the New Zealanders are now in a precarious position, probably needing to win their remaining Super Eight matches against Pakistan and England to advance to the semifinals.
New Zealand's response effectively seized up midway through when key batsmen Jesse Ryder and Ross Taylor both looped simple catches to the infield in the space of three overs. Opener Ryder top-scored with 33 off 28 balls while Taylor's dismissal for 19 left New Zealand needing 83 off less than eight overs with six wickets remaining.
They struggled to stay in touch against a tight South African attack and only some bright hitting from Nathan McCullum, who was unbeaten on 26 off 17 balls, improved their stocks although victory was always unlikely over the closing stages.
Martin Guptill fell for 18, Scott Styris for 13 and Gareth Hopkins for 18 as the New Zealanders failed to push on through the middle stages, with six of the seven dismissals falling to catches in the outfield, not helped by a pitch lacking pace.
South African captain Graeme Smith opted to bat first but the innings didn't accelerate until the closing stages, where they compiled 62 runs off the final five overs.
The New Zealand bowlers were too full to Morkel in particular as the big-hitting left-hander raced to 40 off 18 balls.
He was well supported at the death by an unbeaten 47 from AB de Villiers while Jacques Kallis struck 31 and Herschelle Gibbs 30 at the top of the order.
Captain Daniel Vettori was the pick of the New Zealand bowlers, taking none for 21 off his four overs to put the brakes on through the middle stages.
The most expensive was seamer Tim Southee, who took one for 39 off three and was on the receiving end of Morkel's late swinging.
Earlier today England won the first match on New Zealand's side of the Super Eight draw, beating Pakistan by six wickets courtesy of an unbeaten 73 from Kevin Pietersen.
The New Zealanders face Pakistan in Bridgetown on Sunday (NZT) and England at St Lucia on Tuesday.
