A 22-run triumph left the host nation fuming at Centurion with Proteas skipper Graeme Smith incensed he was not allowed to use a runner as the match drew to a close.
After England notched up 323-8, South Africa could only muster 301-9, 12 runs below the score required to remain in contention for qualification based on net run-rate.
Owais Shah top scored with 98, hammering six sixes along the way, while wicketkeeper Eoin Morgan weighed in with five sixes in his 67, claiming his half-century from only 26 balls. Paul Collingwood contributed an excellent 82 as England set a big target.
However, Smith produced a captain's innings to keep his side's hopes alive, smashing 141 despite opposite number Andrew Strauss denying him runner AB de Villiers with the left-hander suffering from cramp.
James Anderson and Stuart Broad took three wickets apiece but Smith was far from happy with Strauss's behaviour afterwards.
"From my perspective it seemed a little bit inconsistent," said Smith. "Players have got runners for cramp in the past and there needs to be a level of consistency there.
"The thing I have learned from this game is that the world is round and it is going to come back somewhere in his captaincy.
"It will be interesting to see how he handles it if it happens again. It was a crucial part of the game, I had been on the field for 95 overs and had cramped up."
Strauss, who reprieved Angelo Mathews of Sri Lanka from a run-out following a collision last week, was unrepentant.
"He asked me for a runner because he was cramping, the umpires were not particularly keen to give him one, and I felt at the end of a long game when you have had a long innings, you are going to be tired," said Strauss.
"That is one of the things that happens and cramping to a certain extent is a preparation thing and, to a certain extent, a conditioning thing.
"I didn't feel he merited having a runner at that stage. My personal view is you shouldn't get a runner for cramps full stop."
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