Australia lead the Super Eights table with 12 points from six matches, followed by New Zealand (10/6), Sri Lanka (8/6) and South Africa (8/7).
When asked whether his team had finally shed the chokers' tag, Smith said: "I guess I can say yes. It was a big question (before the game).
It was a big pressure day and I think we really demolished it."
South Africa had earned the dubious "chokers" tag after losing pressure matches in the past, but this time they raised the level of their performance when it mattered most.
Smith said his team needed to keep the momentum irrespective of who they play in the semi-final in St Lucia on April 25 where the pitch is expected to be low and slow.
However, it looks more than likely that they will face defending champions Australia for a place in the final.
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"A semi-final is a semi-fi