South Africa produced an unconvincing performance with the bat but beat Zimbabwe by five wickets to set up a semi-final against New Zealand.
An 18-ball 42 from Dewald Brevis at number four proved crucial as wickets tumbled in South Africa's chase of 154 before George Linde (30 off 21) and Tristan Stubbs (21 off 24) saw them over the line with 13 balls to spare.
South Africa, who have won all seven of their matches in this tournament, are searching for a maiden T20 World Cup title having previously reached the final in 2024.
The result also confirms England, who finished top of Group 2 in the Super 8s, will face India in the last four.
"South Africa are going to be hard to stop. They have ticked every box in this tournament," said former Australia wicketkeeper Ryan Campbell on BBC Radio 5 Sports Extra.
"They have a massive belief around the group and are starting to bask in the glory of their younger players who have developed.
"Today was about getting sometime under the belts of the back-ups in case some players need a rest."
