The victory will come as a major morale booster for a South Africa side that have not won a trophy this season but remain in the hunt to change that in the coming week.
Quinton de Kock decided that his team will bat first after winning the toss.
"He (de Kock) has pounced on that as it's gone far".
Australia needed 17 off the last over.
Reeza Hendricks Returns To South Africa T20 SquadCricket South Africa wrote on Twitter, "Hendricks joined the team on Saturday evening in preparation for the second fixture in Port Elizabeth today".
After that, Kagiso Rabada bowled an excellent penultimate over, conceding just 3 runs and Anrich Nortje defended the remaining 17 runs easily.
But in a remarkable display of athleticism, Smith jumped into the air and tapped the ball back into the field with one hand before crashing to the ground.
With Keshav Maharaj sitting atop the domestic one-day cup wicket charts, Tabraiz Shamsi's white-ball role could be coming under pressure but he ensured he answered questions about his suitability to contain with a miserly spell at St George's Park.
But Australia could only muster a run-a-ball 30 from the closing overs, losing four wickets for 20 runs and leaving Warner stranded as he was starved of the strike.
Haysman then facetiously pondered: "Why didn't he catch it?"
Smith nearly did it again to dismiss Miller off the final ball of the innings but spilled the juggling effort when he tripped over the boundary rope. If not for a small hurdle from the cushioning of the boundary rope, Smith would have taken the catch on the second go and van Biljon would have been out. "It was always going to be more hard towards the end".
De Kock brought up his sixth T20I half-century and smashed five fours and four sixes during his stay at the crease. Tell you what, you thought that was gone for six, the crowd thought that was a six, what about that? England were shackled by disciplined bowling until Natalie Sciver (50) upped the ante in the backend of the innings, but their total ultimately proved not enough. Both and a combination of a few other things.
South Africa took wickets in the 18th, 19th and 20th overs to defend a modest total of 158-4 and win the second game by 12 runs at Port Elizabeth's St. George's Park.
Australia's innings followed a similar pattern. It has to be kept in mind that they scored 22 runs in just two of those five overs showing how brilliant a couple of Aussie bowlers were. The had the brakes applied by Dwaine Pretorius, who operated nearly as a second spinner would, bowling offcutters and slower balls galore and Shamsi. Australia, with Warner controlling things, was seemingly set for victory.