The experienced Marizanne Kapp picked up a maiden five-wicket haul to help South Africa restrict the 2017 champions to 235 for nine after putting their opponents in to bat at Mount Maunganui.
The 32-year-old then returned to the crease with the bat to contribute a crucial 32 off 42 balls as South Africa chased down their target with four deliveries to spare to register their third consecutive victory.
Opening batter Laura Wolvaardt lived a charmed life and survived a number of missed chances to top-score for South Africa with a 77 with Kapp taking the side closer to victory before being dismissed in the penultimate over.
“It’s pretty painful losing three close games in a row,” England captain Heather Knight said at the presentation.
“I guess at times we shot ourselves in the foot with the fielding, a batter like Wolvaardt, you can’t give her that many opportunities or she’ll make you pay.
“We’re pretty gutted with the situation, it’s not through lack of effort or a lack of graft. We’re going to have to keep believing that we’ve got a small chance of making it through.”
England, who earlier lost to Australia and the West Indies in their first two matches, still have a mathematical possibility to advance to the semi-finals but would also need other results in their favour.
They will next play India at the same venue on Wednesday.
The victory took South Africa, who will meet hosts New Zealand next on Thursday, to second in the table behind Australia.
“Every day she steps onto the field she shows her class and I think she’s the inspiration for many young girls and boys out there,” South Africa captain Sune Luus said referring to Kapp’s all-round show.
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