The reigning World Twenty20 champions, who've now lost all three of their group matches so far this tournament, posted the sixth lowest completed one-day international total in women's cricket.
Chedean Nation, with 26, was the only West Indies batsman to make double figures as South Africa captain Dane van Niekerk became the first bowler, in either men's or women's international cricket, to take four wickets without conceding a run in her final figures.
Kapp took four for 14 and van Niekerk an astonishing four for none in 3.2 overs.
"It was quite surreal, if I could script it I would not have written it like that," said van Niekerk. "We had our plans coming into the game and it worked to the tee.
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"I'm really proud of the bowlers, especially my two opening bowlers, they were world-class."
To make matters even worse for the West Indies, they dropped both South Africa openers off successive balls.
The end of the match saw West Indies star batsman Deandra Dottin, out for a duck to Kapp, in tears.
"I think their bowling was very good, it's a good bowling line-up, they have a lot of strong players. But from our side, we just needed to execute our skills much better," said West Indies opener Hayley Matthews, out for four. "The wicket had a little grass on it, but the openers bowled really well today."