They restricted the South Africans to 99, then classy allrounder Sophie Devine followed her three for 16 with a rapid unbeaten 27 to hurry New Zealand home.
"I don't think there's any real secret," captain Suzie Bates said. "We're just confident with the group of players we've got. The bowling lineup is really balanced and our batting is experienced and in good form."
Devine, a dual international having been a Black Sticks hockey representative in 36 matches, reckons New Zealand's finals experience will help tonight.
"Most of our team have experienced being in a final, whether on the world stage or ... domestically. If we can perform to the best of our ability, we are going to be a very hard team to beat," she said.
That said, nothing is being taken for granted.
"We earned the right to play the next game but nothing further," Devine said. "So we know we've got to turn up again."
Left-armer Morna Nielsen, with a compelling economy rate of 3.1 per over in the championship, pointed to the improvement in the last 18 months in the fielding performance. She puts much of that down to the planning of Bates and Devine.
"Certainly it's come a long way, but it's also finding where the key fielders need to be, so we give ourselves a chance of stopping runs or taking a wicket. That's something Suzie and Sophie have worked very well on," Hamilton-born Nielsen said last night.
No bowler has taken more wickets than the nine at just 6.77 runs apiece of spinner Leigh Kasparek, and Bates' 171 runs at 42.25 and strike rate of 116.31 are matched only by England's Charlotte Edwards, whose 171 have come at an average of 57.
New Zealand's record against the West Indies is solid. They have won eight of 13 T20 clashes against them and lost three, with one tie and one no result. They last met in the shortest form in St Vincent in September 2014.
The West Indies rely heavily on two players: Stafanie Taylor, who had a season with Auckland and was the International Cricket Council's women's T20 player of last year; and big-hitting allrounder Deandra Dottin.
If New Zealand can do a containing job on them, they will have taken a big step towards the final.
"It's pretty simple," said Nielsen. "You turn up and everyone plays their roles. There is [confidence having] played pretty good cricket."
Women's semifinals:
• England v Australia, Delhi, played 10pm last night
• New Zealand v West Indies, Mumbai, 10pm tonight, live on Sky
Men's semifinals:
• New Zealand v England, Delhi, 2.30am today
• India v West Indies, Mumbai, 2.30am tomorrow
• Path to the women's final
New Zealand:
• bt Sri Lanka by seven wickets, Delhi
• bt Ireland by 93 runs, Mohali
• bt Australia by six wickets, Nagpur
• bt South Africa by seven wickets, Bangalore
West Indies:
• bt Pakistan by four runs, Chennai
• bt Bangladesh by 49 runs, Chennai
• lost to England by one wicket, Dharamsala
• bt India by three runs, Mohali.