The world champions, chasing 247 in 50 overs to win the day-night match, reached their target with five balls to spare after tail-ender Stuart Clark compiled a priceless undefeated 16.
Australia looked poised for a much easier victory when Adam Gilchrist [ Images ] (45) and Simon Katich [ Images ] (46) put on 87 for the first wicket and when Andrew Symonds [ Images ] was in full flight.
Hitting the ball with ferocious power, Symonds cracked two sixes and nine fours to race to 76 off 71 balls.
Roger Telemachus, who had figures of three for 34, set up the thrilling finish when he bowled Symonds to leave Australia at 218 for seven.
Clark and Bracken shared a stand of 23 for the ninth wicket.
"It shows how close the teams really are and it sets up a massive decider at the Wanderers [in Johannesburg] on Sunday," home skipper Smith told a news conference.
"I thought they [Australia] were the team that were chokers, if that's the word, at the back end [of matches]."
Ponting reacted strongly to the remarks.
"He said that, did he?", the Australia captain asked reporters after being told of Smith's opinion. "We won the game, maybe they should look at their own performance.
"That will give us ammunition for Sunday. They can say what they like, they can keep talking it up and losing games."
Defeat was a bitter pill to swallow for South Africa especially after they had gone 2-0 up in the series.
To add to their worries, all rounder Shaun Pollock [ Images ] left the field with a back strain after bowling only five overs.
"It is a concern, it was a huge loss," Smith said. "It meant myself and [Justin] Kemp had to bowl when we didn't want to."
Australia took 19 runs off Smith's off-spinners in the 38th over.
Earlier, South Africa opener Boeta Dippenaar struck his fourth century in one-dayers.
He scored 101 in 141 balls after left-arm seamer Bracken had struck twice early on, having Graeme Smith and Herschelle Gibbs [ Images ] caught behind for a single apiece.
AB de Villiers [ Images ] registered four boundaries and two sixes in his 38 to help Dippenaar revive South Africa after they had slumped to nine for two.
Pollock and Dippenaar also added 72 for the seventh wicket in 9.1 overs.
The all rounder raced to a 28-ball half-century and struck paceman Lee for four successive boundaries.
Pollock finished 53 not out as South Africa made 246 for nine. Bracken and Lewis picked up two wickets apiece.
South Africa Innings
G. Smith c Gilchrist b Bracken 1
B. Dippenaar c Clarke b Lee 101
H. Gibbs c Gilchrist b Bracken 1
A. de Villiers lbw b Lewis 38
J. Kallis c Hussey b Symonds 21
M. Boucher c Gilchrist b Lewis 19
J. Kemp lbw b Clark 1
S. Pollock not out 53
R. Telemachus run out 0
A. Hall run out 0
Extras (b-2 lb-2 w-2 pen-5) 11
Total (for 9 wickets, 50 overs) 246
Fall of wickets: 1-1, 2-9, 3-81, 4-118, 5-170, 6-173, 7-245, 8-246, 9-246.
Did not bat: M. Ntini
Bowling: B. Lee 10-0-55-1, N. Bracken 10-2-36-2, S. Clark 10-1-49-1, M. Lewis 10-0-38-2, A. Symonds 6-0-31-1 (w-1), M. Hussey 2-0-15-0, M. Clarke 2-0-13-0 (w-1)
A. Gilchrist c AB de Villiers b Kallis 45
S. Katich c Kallis b Hall 46
R. Ponting c Boucher b Telemachus 7
D. Martyn c Boucher b Telemachus 1
A. Symonds b Telemachus 76
M. Clarke c Boucher b Kallis 7
M. Hussey run out 19
B. Lee c Boucher b Ntini 6
N. Bracken b Hall 7
S. Clark not out 16
M. Lewis not out 4
Extras (b-1 lb-2 nb-3 w-7) 13
Total (for 9 wickets, 49.1 overs) 247
Fall of wickets: 1-87, 2-99, 3-100, 4-101, 5-140, 6-192, 7-218, 8-218, 9-241.
Bowling: S. Pollock 5-2-22-0 (nb-1), M. Ntini 10-1-50-1, A. Hall 9.1-1-52-2, R. Telemachus 10-1-34-3 (nb-2), J. Kallis 9-0-46-2 (w-3), J. Kemp 4-0-17-0, G. Smith 2-0-23-0 (w-4)
Result: Australia won by 1 wickets