The world's top-ranked outfit came under under-fire after their crushing 281-run defeat in the opening Test, but Smith was proud at the way his players responded as they set up a thrilling third and final match in Cape Town on Saturday.
"We have had to draw on past experiences in this match to find a way to win," he told reporters after South Africa bowled Australia out for 216 in their second innings on the fourth day.
"It has been a difficult week for us after the Pretoria Test. We knew we needed to be smart and clinical and work on good ideas on how we could respond.
"I would say not many teams could respond in the way we did, but it is something this side has done before.
Having set a daunting victory target of 448, South Africa were on the back foot when the tourists raced to 126 without a loss, but fired-up paceman Dale Steyn suddenly got the ball to reverse-swing and claimed four victims as Australia lost 10 wickets for 90 runs.
"Dale always ranges from very angry to extremely angry when he bowls," Smith joked. "But it was a hell of an effort from all the bowlers.
“The intensity they showed with the ball on a wicket that did not do that much was amazing. To get nine wickets in a session is remarkable.
"We always know Dale is one spell away from being able to create something for us. It is great to see that when the game is on the line, he can respond like that."
Smith, though, was annoyed with the number of catches his side put down in Port Elizabeth.
"We actually took about 28 wickets in this Test which is a great effort from our bowlers.”
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