Australia rode on a strong bowling performance to reduce South Africa to 194/6 in their second innings and take the upper hand at the end of the third day of the third cricket Test at the Adelaide Oval here on Saturday.
Off-spinner Nathan Lyon was the most successful among the Australian bowlers with figures of 3/48 while fast bowler Mitchell Starc returned 2/71.
Josh Hazlewood clinched the prized wicket of the experienced Hashim Amla for figures of 1/22.
Opening the innings along with Dean Elgar, Cook dug in and batted through the innings in tough conditions to post a valuable half-century.
He was unbeaten on 81 runs at the close with seven boundaries adorning his 199-ball stint at the crease. De Kock was yet to open his account.
Starc struck first for Australia in the opening over as Elgar was caught at second slip by Steven Smith without opening his account.
Cook then added 81 runs along with Amla before Hazlewood ended their partnership.
Hazlewood produced a beautiful outgoing delivery which kissed the edge of Amla's bat on its way to wicketkeeper Matthew Wade. Amla, who was dropped by Matt Renshaw off Starc on 13, decided to call for a review but to no avail.
The experienced right-hander, who scored 45 runs off 80 balls, has yet to score a half-century in the ongoing series and has been dismissed by Hazlewood five times in the series.
The dominance of the Australian bowlers and the consequent drying up of runs seemingly got to Jean-Paul Duminy who tried to hit Lyon across the line only to see his off-stump uprooted.
Starc got the big wicket of South Africa's in-form stand-in skipper Faf du Plessis soon after with an excellent delivery with a diving Peter Handscomb pulling off the catch at gully.
Lyon then sent back Temba Bavuma, caught by Smith at first slip, and trapped Kyle Abbott leg before in his last two overs of the day to give Australia the advantage going into the fourth day.
Earlier, Usman Khawaja top scored with 145 as Australia were all out for 383 runs in their first innings.
Khawaja, who batted over three days and 466 minutes, hit 12 boundaries over the course of his 308-ball innings. He was finally sent on his way after being trapped leg before by pacer Vernon Philander.
It was his fifth Test century in the past year. He has now scored 314 runs at 62.80 in five innings.
Starting the day the hosts added 100 runs from their last four wickets.
Starc's 91-ball 53, which featured five fours and a six, was his seventh Test half-century. He entertaining innings came to an end when he offered a return catch to pacer Kagiso Rabada.
Lyon chipped in with 13 before becoming Tabraiz Shamsi's maiden Test wicket, while Hazlewood was unbeaten on 11.
Abbott was the best among the South African bowlers with figures of 3/49 with Rabada claiming 3/84.
South Africa: 259/9 declared and 194/6 (Stephen Cook 81 batting; Nathan Lyon 3/48) vs Australia: 383 (Usman Khawaja 145, Steven Smith 59, Peter Handscomb 54; Kyle Abbott 3/49, Kagiso Rabada 3/84).
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