Reigning champions New Zealand survived a scare from South Africa before a second-half rally took them to a 46-17 win in a Women's Rugby World Cup quarter-final on Saturday.

The Black Ferns are the record six-time Women's World Cup winners and have not lost a match at the tournament since 2014.

South Africa, unlike their four-time world champion men's team, were appearing in their first quarter-final.

Yet, at half-time the Springboks were level at 10-10 and threatening a huge -- and rare -- upset at a World Cup dominated by lopsided wins for the top teams.

New Zealand replied with 29 unanswered points to put the result beyond doubt and set up a semi-final with either Canada or Australia, who play later on Saturday.

Kaipo Olsen-Baker was one of three New Zealand players to score two tries.

The No 8, the player of the match, feared her World Cup might be over when she was carried off on a stretcher with an ankle injury in New Zealand's tournament opener against Spain.

"It is definitely not the World Cup I had hoped for, but I am so grateful to all the medical teams and the girls," Olsen-Baker told World Rugby.

- South Africa 'deserve to be here' -

South Africa No 8 Aseza Hele, meanwhile forecast a bright future for her side.

"I know the next World Cup, we are going to be special," she said. "We are here and we belong here."

New Zealand coach Allan Bunting paid tribute to South Africa counterpart Swys de Bruin by saying: "For me, just massive respect to Swys and South Africa.

"They've done an incredible job in such a short space of time and what they're doing for rugby and for women in South Africa is massive."

He added: "They threw in some awesome innovation and put us under some pressure but that's a good thing for us at this point in the tournament."

An emotional De Bruin said: "I'm so proud. Look at our girls, look at the passion. They made a difference for millions of girls in South Africa. They have role models."

Despite the result, South Africa still restricted New Zealand to their smallest winning margin of this World Cup, with the Black Ferns having thrashed Ireland 40-0 in their final Pool C match.

"For us to score three tries against the mighty Black Ferns, it's a big honour," said De Bruin.

This match came just hours after the Springbok men's team inflicted a record 43-10 defeat upon arch-rivals New Zealand in Wellington.

"Great game, almost as fulfilling as this morning with our men's side," said De Bruin. "South African rugby is in the right way."

The Springboks stunned the Black Ferns by opening the scoring in Exeter through prop Babalwa Latsha.

New Zealand hit back through tries from centre Theresa Setefano and teenage wing Braxton Sorensen-McGee, but Aphiwe Ngwevu's try levelled the game at half-time to round off a superb opening 40 minutes for South Africa.

The Black Ferns regained the initiative after the break with five tries.

Full-back Renee Holmes scored twice, with Sorensen-McGee, the tournament's top try-scorer, also completing a double. Replacement Katelyn Vahaakolo grabbed New Zealand's last try .

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South Africa fans react to a try by their side against New Zealand / © AFP

South Africa crossed late in the second half through Lerato Makua in what was veteran Springbok captain Nolusindiso Booi's final game after the 40-year-old lock said she would retire following the World Cup.

"I'm so emotional right now but I am also proud of the progress of our team," said Booi. "I feel that we did good and for sure the young generation will push for the final, hopefully next time."