The result means the unbeaten Proteas must beat the West Indies in their final Super Eight match (2:30am SA time), or get a point from a no-result, to reach the semis.
Chris Jordan took four wickets in five balls, including the third hat-trick of the tournament, as England dismissed the USA for 115.
England captain Jos Buttler then made a blistering 83*, hitting Harmeet Singh for five sixes in an over costing 32 runs, as his side raced to 117-0 in 9.4 overs.
By reaching their target so quickly England assured themselves of a place in the last four on net run-rate.
© Agence France-Presse
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