After England secured their place in the last four on Sunday, the game in Antigua was essentially a quarter-final to decide the other side to progress from Group 2.
Chasing a DLS revised target of 123, South Africa wobbled at times but ultimately withstood the pressure and Marco Jansen thumped a six to seal the win with five balls to spare.
Having restricted West Indies to 135-8, the Proteas appeared in control but Andre Russell struck twice in the second over of the chase to leave them 15-2.
The Windies’ momentum was halted immediately, though, by a sudden downpour that kept the players off the field for 75 minutes.
South Africa returned with a new target from 17 overs and a flurry of boundaries quickly put them back in the ascendency.
But with a raucous crowd at the Sir Vivian Richards Stadium urging them on, the West Indies kept fighting with Roston Chase, who made 52 with the bat, taking three wickets.
As the game headed towards a nervy conclusion with South Africa needing nine from seven balls, Kagiso Rabada hit a glorious cover drive for four and Jansen finished the job at the start of the last over.
Earlier, it was South Africa’s spinners who did the damage with the ball with Tabraiz Shamsi taking 3-28.
The Proteas go through top of the group, with England second, and will face the runners-up in Group 1.
It is still unclear which semi-final either team will play in until India’s final position in Group 1 is confirmed, since Rohit Sharma’s side will definitely play their last-four match in Guyana (Thursday, 16:30 BST). The other semi-final is in Trinidad, also on Thursday (01:30).
