The quarter-final victory was the Proteas' first in a knock-out match at a World Cup and earned them a date with New Zealand or West Indies in Auckland next week with a spot in the final up for grabs.
The Proteas will probably have to win the semi-final to finally bury their reputation as World Cup 'chokers' but they went some way to removing the tag with the rout of the 1996 champions, who they restricted to 133 runs off 37.2 overs.