South Africa had won all seven of their games going into the last-four clash, with five of those wins coming in Ahmedabad, but stumbled when faced with a different set of conditions in Kolkata, where the ball did not come onto the bat as smoothly.
They set New Zealand a below-par 170 to win and their opponents easily chased it down with 43 deliveries remaining on the back of Finn Allen’s unbeaten 33-ball 100.
It marked yet another World Cup failure for the South Africans, who are still seeking a first title, but captain Aiden Markram said there was no other option but to look ahead to the next tournament.
"We'll reflect as a group," Markram said. "But I’m very proud of these guys. They played some really good cricket throughout this competition and it was just an unfortunate evening, really.
"The halfway point, we really felt like we had a sniff. But then, as it goes in T20 cricket, their powerplay got off to a flyer, and you can't protect every boundary. They got away, and then from there it was really hard to pull it back.
"All you do is you break down the game and try to find the areas that could have been better. And you get back on the horse and you try and improve as a group and as individuals. And hopefully that puts you in good stead for the future."
South Africa’s next assignment is a five-match T20 series in New Zealand starting on March 15, though only three of the World Cup squad, spinners Keshav Maharaj and George Linde, and all-rounder Jason Smith, will take part.
New Zealand will meet the winner of Thursday's second semi between co-hosts India and England in the final on Sunday.