The skipper brought up his 26th Test ton and his sixth in nine Tests at the Adelaide ground as Australia seized the initiative in a dominant batting performance early on the second day.
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 half-century in the series.
At lunch, Australia had piled on 116 runs in the morning session to be 389 for five, with Clarke unbeaten on 109 and Haddin not out 57. The pair have added 132 runs for the sixth wicket.
In scenes reminiscent of the bad-tempered first Test in Brisbane, Haddin and Stokes sniped at each other after the over and South African umpire Marais Erasmus had to intervene to keep the players apart.
Haddin, who like Clarke averages over 100 in Tests at the Adelaide ground, played positively in a bid to post a challenging first-innings total on the batting-friendly, drop-in pitch.
Clarke darted off for a quick single off Monty Panesar and with Carberry's throw from behind the wicket wide, wicketkeeper Matt Prior could not effect the run out of Haddin on 18.
Haddin, who scored 94 and 53 during the first Test in Brisbane, had another big moment when he hooked Jimmy Anderson only for Panesar to be too slow to take the chance at long leg.
The Australia and England teams wore black armbands and bowed their heads in a minute's silence for Nelson Mandela before the start of the play.
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