Image source, PA Media
New Zealand have not been defeated in a Women's Rugby World Cup game since losing to Ireland in 2014
ByAlastair Telfer
BBC Sport journalist at Sandy Park, Exeter
Women's Rugby World Cup - quarter-final
New Zealand (10) 46
Tries: Setefano, Sorensen-McGee 2, Holmes 2, Olsen-Baker 2, Vahaakolo Cons: Holmes, Sorensen-McGee 2
South Africa (10) 17
Tries: Latsha, Ngwevu, Makua Con: Dolf
World champions New Zealand recovered from a slow start to defeat a spirited South Africa side and seal their spot in the Women's Rugby World Cup semi-finals.
The Springbok Women, appearing in their first quarter-final in the competition, opened the scoring in Exeter through prop Babalwa Latsha.
The Black Ferns responded through centre Theresa Setefano and teenage wing Braxton Sorensen-McGee, but Aphiwe Ngwevu's try levelled the game at half-time to cap a remarkable first-half performance by South Africa.
However, Allan Bunting's side clicked into gear to score five second-half tries to set up a semi-final against either Canada or Australia, who play later on Saturday, on Friday in Bristol.
Full-back Renee Holmes scored twice, with Sorensen-McGee, the tournament's top try-scorer, and number eight Kaipo Olsen-Baker also grabbing two scores.
South Africa managed to finally cross late in the second half through Lerato Makua to finish off a memorable World Cup campaign on a high.
Replacement Katelyn Vahaakolo was the final try-scorer of an entertaining game at Sandy Park.
South Africa's start shocks world champions
The Springbok Women defeated Brazil and Italy to qualify for their first Women's World Cup quarter-final, with their powerful forwards playing a key role.
Ranked 10th in the world, any shock result was likely to again come through more physical dominance and a destructive start by South Africa's forwards was rewarded when Latsha crossed close to the tryline.
New Zealand were at their sparkling best to put 40 points on Ireland in Brighton last Sunday, but that silky handling was not evident in the early stages.
Instead the Black Ferns' opening score was gift-wrapped as Setefano charged down a clearing kick to score.
Far from at their flowing best, Sorensen-McGee, who has scored back-to-back hat-tricks, then crossed in the corner to give the world champions the lead.
With the final play of the first half, centre Ngwevu finished from close range, which initially came from a maul that included the entire South Africa team, summing up their simple but well-executed gameplan.
Olsen-Baker scores try as New Zealand take control over South Africa
Black Ferns show quality
Right from the restart, it was a different Black Ferns.
Errors were instantly cut out as Holmes finished off a flowing move, before Women's Sevens Player of the Year Jorja Miller broke clear to set up Sorensen-McGee.
Olsen-Baker's first try put further distance between the sides after an intelligent kick through by scrum-half Maia Joseph was regathered by Sorensen-McGee, who lost her footing when a third consecutive hat-trick looked a certainty.
Sharp interplay between forwards and backs was finished again by Olsen-Baker, who impressed on her return from injury, with Bunting's side returning to their clinical best.
When on song, New Zealand are lethal and proper contenders to retain the World Cup, but consistent scrum penalties and a slow start will be particularly pleasing for likely semi-finalists Canada, who have some of the best forwards in the tournament.
However, the six-time winners will be pleased with how they overcame some early problems, which should stand them in good stead for harder tests to come.
South Africa lifted captain Nolusindiso Booi, 40, in the air and danced on the Sandy Park pitch at full-time after their tournament goal of playing in the knockout stage was achieved.
Line-ups
New Zealand: Holmes; Sorensen-McGee, Waaka, Setefano, Woodman-Wickliffe; Demant (co-capt), Joseph; Viliko, Ponsonby, Mahutariki-Fakalelu, Roos, Bremner, Mikaele-Tu'u, Miller, Olsen-Baker.
Replacements: Lolohea, Tangen-Wainohu, Henwood, Bayfield, Tukuafu (co-capt), Hohaia, Vahaakolo, Leti-I'iga.
South Africa: Dolf; Samboya, Mpupha, Ngwevu, Malinga; Van Rensburg, Roos; Charlie, Gwala, Latsha, Booi (capt), Lochner, Solontsi, Mcatshulwa, Hele.
Replacements: Hanekom, Ngxingolo, Mdliki, Ubisi, Qolo, Makua, Jacobs, Webb.
Match officials
Referee: Sara Cox (England)
Assistant referees: Ella Goldsmith (Australia) and Kat Roche (United States)
Television match official: Rachel Horton