On a third day at Kingsmead where the Proteas' batters left plenty to be desired, Australia's bowlers stood tall to have the hosts all out for 284 after tea.
Australia's lead could have been more, if not for South Africa's tail wagging and Keshav Maharaj, Simon Harmer and Anrich Nortje adding 87 for the final two wickets.
Regardless, it gives Australia the chance to set South Africa a big fourth-innings target, with lost play due to poor light with an early sunset an ever threat in this match.
Pat Cummins led the way with 3-54 for the tourists, as he, Nathan Lyon, Josh Hazlewood and Mitchell Starc became the first quartet in history to reach 600 wickets in Tests played together.
But this was a rare day where a fielder outshone the bowling.
Smith twice showed his wares to take smart catches at slip off Lyon (2-58), moving to his right before the ball was middled to intercept reverse sweeps.
The first of those removed South Africa's captain Temba Bavuma for three as part of a collapse of 3-15 before lunch, after the Proteas had reached 1-84 at a rapid rate.
And while that was impressive, Smith's second to catch wicketkeeper-bat Kyle Verreynne on 13 was even better.
The former captain again anticipated the shot and moved before Verreynne had struck the ball, before sticking his right hand out catching it one handed.
Sandwiched between those dismissals was another brilliant catch to dismiss David Bedingham on 49, this time with both feet in the air at second slip off Cummins.
That edge would likely have flown to Matt Renshaw at first slip if not for Smith, but it did help him go back past Joe Root's mark of 220 for most career catches.
Smith also took the final catch to wrap up the innings when Beau Webster drew Nortje's edge, taking his personally tally to 223.
Fielding aside, South Africa have themselves to blame for their predicament.
While Renshaw's first-innings 190 was a picture of patience and control for Australia in their 390, the hosts lacked exactly that for large parts of Sunday.
After threatening to stabilise the innings from 4-99, Wiaan Mulder (30) and Tristan Stubbs (32) were both out taking on short balls from Cummins in the space of two overs.
It was hard to determine which stroke was worse.
Mulder appeared to withdraw from his pull shot before ballooning the ball to square leg, while Stubbs' dismissal, hooking at fine leg, was extra frustrating given what had just happened.
Adding to the dismay, Marco Jansen then pulled Hazlewood (2-54) to mid off six overs later after whacking six boundaries in his 26.
The morning had earlier started so well for the Proteas when Aiden Markram and Bedingham scored 62 from the first 10 overs with a flurry of cover drives.
But Australia's experience showed when the quicks pulled back their lengths slightly, Markram edged Starc to slip on 37 and the Proteas lost 3-15 in 10 overs.
