South Africa needed less than a run a ball over the last four overs before a late collapse saw India claim the title.
Both sides head into the final undefeated.
India will face South Africa for the title.
The Proteas will meet the winners between India and champions England.
The rain-affected match against Bangladesh could have seen any of the three teams progress.
The Indians are safely in the semis, but Australia must now pin their hopes on Bangladesh.
The English are on track for the semi-finals.
The Aussies lost their unbeaten record at the tournament.
The Indians have clinched their second 'Super Eight' victory.
South Africa are now top of their group after their tight Super Eight victory over England.
Australia remain unbeaten at the tournament.
India have closed out a 47-run win in Barbados.
The NZ whiteball captain will surrender his leadership role this summer.
New Zealand failed to progress past group play, after opening losses to Afghanistan and West Indies.
New Zealand made light work of Papua New Guinea in their final match of the tournament.
New Zealand play their final match of the tournament.
The result sees the English through to the 'Super Eight' ahead of the Scots.
New Zealand dismissed their rivals for a near-record low score and easily wrapped up the run chase.
The Africans just avoided the lowest-ever score at a World Cup.
The news is the latest drama during a difficult campaign for New Zealand.
