Du Plessis, who finished unbeaten 110 after batting through the last day to save the second test on debut at Adelaide on Monday, shared a 57-run seventh-wicket stand with Robin Peterson (31) to stop a serious slide after South Africa lost five wickets for 14 runs just before and after the lunch interval.
He was not out 39 at tea and No. 9 Vernon Philander was 4.
The South Africans were making careful progress at 61-1 just 15 minutes before lunch until Mitchell Starc struck twice in his last two overs to make it 63-3 at the end of the first session.
The new-look Australian attack took three wickets quickly to make the total 75-6 before du Plessis and Peterson combined.
Shane Watson marked his return from injury by taking the first wicket to remove South Africa skipper Graeme Smith (16) with the total at 38.
Starc, who was 12th man in the drawn tests in Brisbane and Adelaide, bowled opener Alviro Peterson (30) and Jacques Kallis (2) to swing momentum in Australia's favor.
Hashim Amla (11) had a reprieve five balls after the first break when Ed Cowan put down a regulation chance off John Hastings' bowling. But he was out next over, without adding to his score, when he was run out at the striker's end by David Warner's direct hit.
Hastings got a ball to swing out and late in his next over and picked up his first test wicket when A.B. de Villiers (4) edged to Clarke at slip and South Africa slumped to 67-5.
Dean Elgar faced 12 balls on debut before attempting to pull a sharply rising ball from Mitchell Johnson and top-edging down leg side to wicketkeeper Matthew Wade and offspinner Nathan Lyon ended the seventh-wicket stand when he had Peterson out attempting to cut and getting a feint edge to wicketkeeper Matthew Wade.
South Africa only needs to draw the Perth test to retain the No. 1 test ranking. Australia needs a win to replace the tourists at No. 1 and has the extra motivation for winning after Ricky Ponting announced this match would be his last in international cricket. The 37-year-old ex-skipper equaled Steve Waugh's record of 168 test caps when he walked on to field at the WACA.
The Australians made four changes for the deciding match, including the recall for Watson and an unprecedented complete change of the pace attack.
Left-armers Starc and Johnson were recalled and Hastings given his test debut after selectors decided to rest Peter Siddle and Ben Hilfenhaus due to their heavy workload in the Adelaide test after James Pattinson was injured and unable to bowl.
South Africa made three changes from the Adelaide match, with Vernon Philander overcoming a bad back to return at the expense of Rory Kleinveldt, Robin Peterson replaced legspinner Imran Tahir and Dean Elgar will make his debut in place of Jacques Rudolph. Kallis passed a medical test on his injured right hamstring and was declared fit to bat, but won't be bowling in the match.
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