The Proteas beat England by 10 runs in Sharjah but missed out on the T20 World Cup semi-finals on net run rate.
Having posted 189-2 in their 20 overs, South Africa needed to restrict England to 131 runs or fewer to progress to the final four.
They failed to do so, with Australia – who beat the West Indies earlier in the day – qualifying along with England.
The Proteas and Aussies both finished with eight log points, having won four out of five Super 12 games, but Australia’s net run rate (+1.216) was superior to South Africa’s (+0.739).
England, who topped the group when they passed 109, finished on 179-8 after a hat-trick by Kagiso Rabada in the final over. It was England’s first loss in five matches.
Rassie van der Dussen (94* off 60 balls) and Aiden Markram (52* off 25) put on an unbeaten attacking partnership of 103 for the third wicket.
England elected to field first and Moeen Ali struck early after he bowled Reeza Hendricks for two.
Quinton de Kock and Van der Dussen rebuilt the innings with their second-wicket stand of 71.
Adil Rashid sent back De Kock for 34 with his leg spin, but Van der Dussen stood firm and mixed the right dose of caution and aggression to reach his half-century in 37 balls.
He then combined with Markram to take the assault to the opposition bowlers as he attacked Chris Woakes in his fourth over – the 16th of the innings – hitting three sixes between them as 21 runs were added to the Proteas total.
Markram reached his fifty off 24 balls with a six off Chris Jordan as he hit two fours and four sixes.
In reply, England started well with Jason Roy and Jos Buttler hitting boundaries in the first four overs. But Roy suffered a calf-injury issue while taking a run with Buttler and had to be helped off the field.
South Africa seized the opportunity and Anrich Nortje sent back Buttler, for 26, in the next over. Then Tabraiz Shamsi trapped Jonny Bairstow lbw for one.
Moeen, who struck 37 off 27 balls, and Dawid Malan hit back in a partnership of 51 but Shamsi once again put the brakes.
Moeen hit Shamsi for a towering six but got out next ball attempting another big one which instead went straight into the hands of David Miller.
Malan kept up the attack with Liam Livingston, who hit Rabada for three straight sixes, to keep the chase on track despite losing his partner in the next over.
But Livingstone fell for 28 and the South African bowlers took charge. Rabada sent back Chris Woakes, skipper Eoin Morgan and Chris Jordan for the tournament’s third hat-trick.
© Agence France-Presse