The tourists claimed a third successive victory at the WACA after 2008 and 2012 triumphs and a 1-0 lead in the series, which continues in Hobart on Saturday and concludes with a day-nighter at Adelaide Oval.
Australia's batsmen were unable to cope with Rabada's pace and swing as the 21-year-old took his fourth five-wicket haul in his ninth test, making light of the absence of South Africa's injured pace spearhead Dale Steyn.
South Africa declared on 540-8 after lunch on Sunday, leaving Australia with an imposing 539-run victory target or more realistically almost five sessions to bat out for a draw.
The hosts had looked in a strong position on day two when, having dismissed South Africa for 242, they were 158 without loss before collapsing to 244 all out.
(Reporting by Nick Mulvenney in Sydney; Editing by Amlan Chakraborty)
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