Kapp grabbed four for 14 to do the early damage along with new-ball partner Shabnim Ismail while leg-spinner van Niekerk later picked four wickets without conceding a run as South Africa bowled the opposition out for 48 in 25.2 overs. South Africa got to its target in only 6.2 overs.
Captain van Niekerk helped clear up the tail as the West Indies could set just 49 to win, recording the sixth lowest total in Women’s World Cup history.
Openers Lizelle Lee and Laura Wolvaardt made light work of the low target to help complete the victory.
Van Niekerk said: “It was quite surreal, if I could script it I would not have written it like that.
“We had our plans coming into the game and it worked to the tee. I’m really proud of the bowlers, especially my two opening bowlers, they were world class.”
The West Indies top order couldn’t cope with the movement Ismail was producing in the English conditions.
Hayley Matthews was the first to fall to Ismail, trapped leg before wicket for just four runs.
And Ismail struck again in her next over, sending Stefanie Taylor’s off stump cartwheeling.
The West Indies side was in serious trouble as its top order fell apart. Pace bowler Kapp joined the party as she first caught and bowled debutant Reniece Boyce and then trapped Kyshona Knight leg before wicket the next ball.
She may have been denied a hat-trick, but two balls later Kapp had her next third victim as she dismantled Deandra Dottin’s stumps, an incredible three wickets in one over.
A 22-run partnership between Chedean Nation and Merissa Aguilleira was the only resistance offered.
But the brief West Indies revival was ended by van Niekerk when she bowled Aguilleira round her legs as the batter attempted to sweep the spinner.
West Indies continued to try and sweep van Niekerk with little joy as Shanel Dolly shovelled one straight to Laura Wolvaardt.
And after dismissing No.11 Qiana Joseph, van Niekerk became the first woman or man in World Cup history to take four wickets without conceding a run.
West Indies spurned chances to put South Africa under pressure as first captain Stafanie Taylor and then Anisa Mohammed dropped Lee off consecutive deliveries.
The opening batters didn’t look back as they cruised to the target to make it two wins from three in the tournament.
West Indies batter Hayley Matthews said: “We didn’t do too well against them in the first game, we wanted to start fresh but we went out there and just weren’t able to execute our skills.
“I think their bowling was very good, it’s a good bowling line-up, they have a lot of strong players. But from outside we just needed to execute our skills much better.
“The wicket had a little grass on it, but the openers bowled really well today.”
South Africa beat West Indies by 10 wickets at Grace Road, Leicester
West Indies 48 all out in 25.2 overs (Chedean Nation 26; Dane van Niekerk 4-0, Marizanne Kapp 4-14, Shabnim Ismail 2-16)
South Africa 51 for no loss in 6.2 overs (Lizelle Lee 29 not out, Laura Wolvaardt 19 not out)
Player of the match: Marizanne Kapp (South Africa)
Next matches – England v South Africa, Bristol County Ground, Bristol, 5 July; West Indies v New Zealand, The County Ground, Taunton, 6 July