Skipper Clarke claimed his third century in five Ashes Tests and his 26th overall, while vice-captain Haddin smashed four sixes in his fourth Test ton to help the home side declare at 570 for nine.
Johnson, hurling down 150 km/h (93 mph) thunderbolts, knocked over Cook for three in his second over to ram home Australia's advantage.
By the close of the second day, the tourists were hanging on against a hostile Australian attack at 35 for one with Michael Carberry on 20 and Joe Root, who took one on the chest from Johnson, not out nine.
It was very much Australia's day as Clarke and Haddin put on 200 runs -- the highest sixth-wicket stand in all Tests in Adelaide, eclipsing the 191 shared by Imran Khan and Wasim Akram for Pakistan in 1990.
Clarke continued his love affair with the Adelaide Oval with his sixth century in nine Tests at the famous ground, while Haddin brought up his third Ashes hundred.
Clarke, dropped by Ian Bell at short leg on 91, played the captain's knock while Haddin chanced his luck to bring up his third consecutive score over 50 in the series.
Cook was beaten by Johnson's sheer pace with his off-stump knocked back by a beautiful swinging delivery to a huge roar from the 35,000 Adelaide crowd.
It was Australia's positivity from the day's opening over that swung the match after it was even-stevens on the opening day.
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