Left-arm wrist-spinner Tabraiz Shamsi (3 for 6) and gangling pacer Marco Jansen (3-16) spearheaded the rout of Afghanistan's brittle batting line-up for just 56 off 11.5 overs after they chose to bat.
Fast bowlers Kagiso Rabada and Anrich Nortje maintained the relentless pressure with two wickets apiece at the Brian Lara Stadium in Trinidad.
On a surface which encouraged all bowlers but left Afghanistan with too little to defend, South Africa lost Quinton de Kock early in reply for Fazalhaq Farooqi's tournament-leading 17th wicket.
But Reeza Hendricks (29 not out) and captain Aiden Markram (23 not out) saw them to victory at 60 for one off 8.5 overs to advance the Proteas to Saturday's final in Barbados where they will face the winners of Thursday's second semi-final between title-holders England and unbeaten India in Guyana.
"We assessed pretty early that the wicket was giving us something to work with so it was just about sticking to our plans, keeping it simple and getting the results," Man of the Match Jansen said of South Africa's bowling display, which effectively ended the match as a contest.
Only Azmatullah Omarzai (10) got into double-figures for the Afghans while their highest contribution to the paltry total was 13 extras in a thoroughly deflating effort following Monday's pulsating drama when they pipped Bangladesh in St. Vincent to reach the final four.
Throughout this dream run to their first semi-final of a senior men's world tournament Afghanistan have been reliant on openers Rahmanullah Gurbaz and Ibrahim Zadran to give them a solid platform and at the same time mask the frailties of the rest of the batting line-up.
'A tough night for us'
But when Jansen had Gurbaz taken at slip by Hendricks without scoring in the first over of the match, the worst fears of the Afghans and a growing mass of supporters in the Caribbean were realised as the Proteas mercilessly exploited their opponents' technical deficiencies.
"It was a tough night for us as a team, but that how it goes in T20s," said Afghan captain Rashid Khan.
"You need to be mentally ready for any kind of situation. They bowled exceptionally and we just couldn’t bat well."
For Markram, who led South Africa to the Under-19 men's title in 2014 in Dubai, it was all about making the most of good luck.
"I was fortunate to have lost the toss, I guess, because we also would have batted. But still the bowlers had to get it in the right areas and they did that," he explained.
"It's not really the captain who gets you to this stage of a competition. It's a massive squad effort involving those behind the scenes and off the field."
This will be South Africa's first senior men's final since the inaugural Champions Trophy in Bangladesh in 1998 when the side led by Hansie Cronje defeated Brian Lara's West Indies team in the title match.
Afghan skipper Rashid meanwhile said his team would look back on their campaign pride and belief for the future.
"We came here before the tournament and if you told us we would be playing the semi-final against South Africa, we would accept that," Rashid said. "We are capable of beating any side.
"Next time when we participate in a tournament like this, we will have the belief. It's about how you manage yourself in those pressure situations against tough teams.
"There is a lot of hard work to be done, especially in the middle order...We have achieved some good results but when we come back in the tournament, we need to do better, especially in the batting department."
