After winning the toss and opting to field first on Friday, England got off to a sensational start, skittling the Proteas for just 69 with Linsey Smith the pick of the bowling attack as she took 3-7.
Sinalo Jafta was the only batter to reach double figures in a bleak display from the South Africans, while Tammy Beaumont and Amy Jones eased to their 70-run target in just 14.1 overs to claim a first win of the competition.
England's attention now turns to their next game, which takes place on Tuesday against Bangladesh.
In an extraordinary start, South Africa skipper Laura Wolvaardt was caught and bowled by Smith in the second over before the spinner claimed her second scalp in the fourth by bowling Tazmin Brits.
Seamer Lauren Bell castled Sune Luus the following over and Smith soon bagged her third, bowling the danger woman Marizanne Kapp as South Africa slumped to 4-19.
Captain Nat Sciver-Brunt then dismissed Anneke Bosch and Chloe Tryon in quick succession, and the wickets just kept tumbling as Nadine de Klerk was then caught by Heather Knight off Sophie Ecclestone.
England's spinners were able to quickly finish off South Africa's innings inside 21 overs when Charlie Dean bowled both Masabata Klaas and Nonkululeko Mlaba either side of Ecclestone's dismissal of Jafta, who had provided the only resistance with her stubborn 22.
The England openers made light work of the chase, Jones ending up unbeaten on 40 and and Beaumont 21no.
"To get that start was really special and we are delighted with how we went," player of the match Smith said after England's third 10-wicket win the history of the Women's World Cup.
"Most importantly we got a big win today. I was told yesterday that I would open the bowling and I was excited about it. It is a tough challenge, but conditions suited me today. I am lucky I could do well."
"It was not our best day with the bat, but we haven't become a bad batting unit overnight," Wolvaardt said.
"We still have a long tournament ahead of us and will look to put this loss behind us as quickly as we can."
South Africa next play New Zealand in Indore on Monday, while in the tournament's Saturday fixture, co-hosts Sri Lanka will play defending champions Australia in Colombo.
With PA
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