In reply, South Africa had been 15/2 in two overs when rain stopped play.
The match was truncated by three overs with South Africa being set with a revised goal of 123 in 17 overs.
The Proteas chased that down in 16.1 overs to knock the hosts out and grow to be the second workforce to qualify for the final 4 stage within the World Cup.
Defending champions England had been the primary workforce to qualify for the semifinals.
Brief Scores: West Indies: 135 for 8 in 20 overs (Roston Chase 52, Kyle Mayers 35; Tabraiz Shamsi 3/27)
South Africa: 124 for 7 in 16.1 overs (Tristan Stubbs 29, Heinrich Klaasen 22; Roston Chase 3/12, Andre Russell 2/19)