The White Ferns have lost to South Africa for the first time at a Cricket World Cup, losing in agonising fashion in the last over at Hamilton's Seddon Park.
New Zealand now need to win their remaining two matches and hope other results go their way in order to qualify for the semi-finals.
They face England at Eden Park on Sunday and then Pakistan in Christchurch on Saturday week.
South African star Marizanne Kapp was inspirational as she guided the Proteas home in the pursuit of New Zealand's total of 228.
The all-rounder scored 36 from 35 balls before Ayabonga Khaka hit the winning run with three balls to spare.
The White Ferns will rue collapsing to be bowled out for 228 in the key clash.
New Zealand were led by a brilliant 93 from captain Sophie Devine and were well-placed for a total in excess of 250 at 197/4 after 40 overs, but it would go horribly wrong after Devine was dismissed.
Devine was bowled trying to clear the boundary a second time in as many balls, sparking a dramatic collapse of 6 for 30.
Brooke Halliday (24), Katey Martin (9), Hannah Rowe (0), Lea Tahuhu (0) and Jess Kerr (6) were all dismissed in quick succession after their captain was bowled.
The wicket of Martin, who was bowled by Shabnim Ismail, sparked a fiery send-off from the South African, with the New Zealand wicketkeeper looking back and appearing to make the symbol for crazy.
In the third over of a see-sawing innings, New Zealand lost Suzie Bates, who was bowled through the gate by Ismail, while driving loosely.
That brought Amelia Kerr to the crease, who combined for an 81-run stand with captain Sophie Devine.
After starting cautiously, the pair were threatening to lead New Zealand to a big score, when Kerr fell to South African captain Sune Luus in the 19th over for 42.
The New Zealand all-rounder would be disappointed with her LBW dismissal after she missed an attempted sweep of a full toss from the leg-spinner.
The innings was left in a precarious position after Amy Satterthwaite fell just three balls later, caught behind off Khaka trying to cut a delivery that was probably too full and close for the shot.
From 88/3, Devine would combine with Maddy Green for an 80-run stand for the fourth wicket, during which the White Ferns captain brought up her 50 from 61 balls.
After struggling to score early in her innings, Green moved through to 30 from 58 balls when she was run out by a good throw from Laura Wolvaardt as the New Zealand pair attempted a quick single to point.
Devine would depart for 93, sparking the dramatic collapse.
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