The Dutch, runners-up in 2019, will now face Spain in the last eight but they suffered some anxious moments in front of 40,000 fans in Sydney and had goalkeeper Daphne van Domselaar to thank for making several important saves in the first half.
Jill Roord scored after nine minutes to put the Dutch on their way against a team that sits 45 places below them in the world rankings and was featured in the knockout rounds for the first time.
South Africa goalkeeper Kaylin Swart then made a mess of an innocuous Lineth Beerensteyn shot midway through the second half to gift the Dutch a second.
The African champions will be kicking themselves after having numerous chances in the opening 45 minutes, almost all of them falling to their livewire captain Thembi Kgatlana.
Midfielder Roord nodded in the opener from close range following a corner for her fourth goal of the tournament.
The Netherlands then stood firm before adding their second goal on 68 minutes when Swart’s blunder let Beerensteyn’s tame effort slip through her hands.
“Daphne saved us a few times and I was happy to lead 1-0 at half-time,” said Dutch coach Andries Jonker.
“We did much better in the second half and had much more control of the game.
“We deserved to score again and in the end deserved to win.”
His team will now return to New Zealand for Friday’s last-eight game in Wellington against Spain, who outclassed Switzerland 5-1 on Saturday.
South Africa coach Desiree Ellis was proud but felt her side should have won.
“We had a lot of chances, especially in the first half, to kill off the game,” she said.
“The chances we created should have put us out of sight.”
‘Lucky USA’
The USA go into their meeting with Sweden in Melbourne, which kicks off at 0900 GMT, looking to improve on some lacklustre performances in the group stage as they chase an unprecedented third consecutive World Cup title.
After Germany’s shock group-phase exit, the top-rated Americans and Sweden, third on the FIFA list, are the two highest-ranked teams left standing.
The winners will go through to a quarter-final against Japan in Auckland on Friday.
Vlatko Andonovski’s USA have looked unconvincing, squeezing into the knockout phase with a 0-0 draw against debutants Portugal and also being held by the Netherlands.
“The fact we are in, we are lucky, but we are moving on,” Andonovski said on the eve of the game.
“Now we will do everything possible so that same situation doesn’t happen again. We are doing everything we can to provide success and meet the expectations for everyone.”
The United States and Sweden are familiar foes, having met six times before at World Cups, but never in the knockout stages.
The USA won their last World Cup encounter 2-0 in 2019 on their way to the title, but Sweden were 3-0 winners when they last met at the Tokyo Olympics.
Coach Peter Gerhardsson said history will mean nothing when they meet and is confident the underperforming champions can be beaten.
“It’s not something I look at, historical facts, I’m rooted in the present,” he said.
“There are a lot of new players in both line-ups so history is less important.
“(The Olympics) was two years ago, it’s all about the physical and mental shape we are in now,” he added.
“I have great confidence in the squad. We believe in this, believe we can win.”
Japan have been the sensation of the tournament so far and the 2011 champions eased into the last eight with a 3-1 win over Norway on Saturday in Wellington.
Monday’s action sees European champions England take on Nigeria in Brisbane before co-hosts Australia face Denmark in Sydney.
