South Africa were 39 for one at the close.
Rabada was the chief destroyer in the Australia first innings with 5-96, including a burst of 5-13 off 18 balls.
The incident happened after Rabada scalped Smith's crucial wicket for 25 and celebrated the victory by brushing his shoulder against the departing skipper.
If Rabada is handed a ban it will be a big blow to the hosts, a fact his pace bowling partner Vernon Philander highlighted while speaking to the press.
Rabada is no stranger to improper behaviour, he now has five demerit points to his name and another three will see him sit out two Tests as a tally of eight demerit points within a 24-month period warrants such a penalty, per ICC rules. If found guilty of such a charge, a minimum of three demerit points are applied.
He was a shining light on a day where the South Africans heard they'll have to chew fingernails over Rabada.
Philander said Rabada's spell was "amazing to watch".More news: Aaron Finch criticises South Africa's role in sledging war with Australia
Kagiso Rabada celebrates Steve Smith's wicket.
But the scoring was painfully slow and Australia were right back in the game when both batsmen were dismissed in the first two overs after tea, followed by two more batsmen being dismissed cheaply.
Starc bowled Amla and Josh Hazlewood had Elgar caught behind eight balls later. It was a day of contrasts.
Brief scores: Australia 243 (David Warner 63, Kagiso Rabada 5/96); South Africa 39/1.
Umpires, having put both captains on notice pre-match to ensure their players behave better compared to the acrimonious first Test in Durban, had a long and stern chat with Proteas captain Faf du Plessis after the incident. He scored his runs off 100 balls with nine fours. With Smith directly in his line of movement, Rabada's shoulder made contact with that of the Australian captain. Australia had five-and-a-half overs with the second new ball late on Saturday but were unable to conjure a wicket.
Lyon admitted that Australia's collapse was disappointing but said he was confident they could fight back.
"We're known for being an aggressive team, but Davey Warner, I've heard him cop everything under the sun and I've never heard him whinge about it once, I've never heard him complain about it".