Before the weekend's action in the Caribbean, South Africa narrowly headed Ricky Ponting's world champions but a shock defeat by Bangladesh on Saturday coupled with Sunday's result reversed the positions, the International Cricket Council said.
Long-time leaders Australia lost their number one spot after crashing to a 3-0 series defeat in New Zealand in February.
Towards the other end of the rankings, England's defeat meant they stayed seventh, two points ahead of the West Indies and three behind India.
If results go the way of the hosts in their remaining World Cup matches, however, they could overtake Michael Vaughan's team before the end of the Super Eights stage of the tournament which finishes on April 28 in Barbados.
Rankings
1 Australia 128 points, 2 South Africa 125, 3 New Zealand 115, 4 Sri Lanka 110, 5 Pakistan 110, 6 India 106, 7 England 103, 8 West Indies 101, 9 Bangladesh 46, 10 Zimbabwe 22, 11 Kenya 0
