On a third day at Kingsmead where the Proteas' batters left plenty to be desired, South Africa were all out for 284 and surrendered a 106-run first-innings lead in the series opener.
Australia then went to stumps at 0-33 and with an advantage of 139 runs when bad light again stopped play, with the under-pressure Nic Maddinson not out on 17.
After a 33-ball first-innings duck drew several questions around his selection, Maddinson hooked his first ball from Marco Jansen for four on Sunday.
He followed it up with another boundary over backward point and flicked Wiaan Mulder for six just before play was stopped, with early sunsets looming as Australia's biggest hurdle for victory.
Pat Cummins had led the way with 3-54 for the tourists on Sunday, 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 and take his person tally to 223, after Keshav Maharaj, Simon Harmer and Anrich Nortje added a crucial 87 for the final two wickets.
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, 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 (2-63) to slip on 37 and the Proteas lost 3-15 in 10 overs.
