The opener thumped an undefeated 119 from 124 balls, the highest score by a South African in a one-dayer against Australia.
The tourists, who won the toss and chose to bat, totalled 229 for eight in a match reduced to 47 overs a side by rain.
South Africa, set a revised target of 204 in 41 overs after more rain, got home in 37.3 overs. Smith's innings included 12 fours and a six and beat the previous record of 112 held jointly by Gary Kirsten and Hansie Cronje [ Images ].
Smith, who faced stinging criticism after his team performed poorly on their tour of Australia, roared with satisfaction after he stroked Michael Clarke [ Images ] through the covers to reach his sixth one-day century.
Clarke and Michael Hussey [ Images ] had resurrected Australia's innings with a century stand after the visitors slumped to 25 for three. Clarke clipped his 53 off 82 balls, while Hussey's 56 came off 73 balls.
Simon Katich [ Images ], who dragged a wide delivery from fast bowler Makhaya Ntini [ Images ] onto his stumps, and Damien Martyn, trapped plumb leg-before by seamer Shaun Pollock [ Images ], fell early on.
That was the signal for Clarke and Hussey to begin their rescuing partnership, and they scored steadily despite a slow pitch and an outfield slowed by overnight and morning rain that delayed the start by 30 minutes.
The second game in the five-match series will be played in Cape Town on Friday.
Australia: (47 overs maximum)
A C Gilchrist c Nel b Ntini 14
S M Katich b Ntini 2
D R Martyn lbw Pollock 1
M J Clarke c de Villiers b Pollock 53
M E K Hussey c Dippenaar b Pollock 56
S R Watson b Hall 22
G B Hogg run out (Gibbs) 13
B Lee not out 38
N W Bracken run out (Boucher/Ntini) 16
M G Johnson not out 0
Extras: (b 1, lb 5, w 8) 14
Total: (8 wickets, 47 overs, 202 mins) 229
Did not bat: M L Lewis.
Fall of wickets: 1-4, 2-5, 3-25, 4-125, 5-132, 6-157, 7-208, 8-227.
Bowling: Pollock 10-1-23-3, Ntini 9-3-42-2 (3w), Nel 10-0-62-0 (4w), Hall 8-0-36-1, Peterson 7-0-36-0, Smith 3-0-24-0 (1w).
South Africa: (target: 204 runs from 41 overs)
G C Smith not out 119
H H Dippenaar b Bracken 10
H H Gibbs run out (Clarke) 0
A B de Villiers c Gilchrist b Hogg 43
M V Boucher run out (Katich/Lee) 4
J M Kemp not out 24
Extras: (lb 1, w 5, nb 1) 7
Total: (4 wickets, 37.3 overs, 172 mins) 207
Did not bat: S M Pollock, R J Peterson, A J Hall, M Ntini, A Nel.
Fall of wickets: 1-24, 2-28, 3-111, 4-134.
Bowling: Lee 10-0-59-0 (1nb, 2w), Bracken 8-1-27-1 (2w), Johnson 3-0-28-0, Lewis 3-0-25-0 (1w), Hogg 8-1-30-1, Clarke 3.3-0-19-0, Watson 2-0-18-0.