South Africa had resumed on 194 for six but lost Quinton de Kock in the third over of the day before the new ball accounted for Vernon Philander, Kagiso Rabada and opener Stephen Cook, who made 104.
Left-arm paceman Mitchell Starc took two of the last four wickets to finish with figures of 4-80.
Australia made 383 in reply to South Africa's first innings 259-9 declared. The tourists won the first two tests in Perth and Hobart to be assured of a third successive Test series triumph in Australia.
ReutersAustralia dismissed South Africa for 250 before tea on the fourth day of the day-night third and final Test on Sunday.
Original source: Aussies chasing 127 for victory in Adelaide