Clarke was unbeaten on 109 at the break with his vice captain Bradd Haddin alongside him on 57 after the pair punished a flagging England attack to add 116 runs to the overnight total in an unbroken stand of 132.
Having dropped three catches on Thursday's opening day, two of which would have dismissed Clarke and Haddin, England's fielders let their bowlers down again on an overcast morning beside the River Torrens.
Haddin could well have been run out for 18 after being called through for a cheeky single by Clarke but was let off by a poor throw back to the stumps by Michael Carberry, who also spilled a simple catch just before stumps on Thursday to save the wicketkeeper.
Haddin was granted another life on 30 by Monty Panesar, who held up rather than take a dive to catch a miscued pull shot off seamer James Anderson just before the drinks break.
Ian Bell also put down a tough chance at short leg when Clarke, on 91, charged down the wicket in a bid to despatch spinner Graeme Swann but succeeded only to nick it behind.
The most glaring howler, though, was from England new boy Ben Stokes who had Haddin caught behind on 51 only to have his maiden Test wicket in his debut match taken away on review when it was shown he had overstepped the mark.
Haddin gave the all-rounder some choice words at the end of the over and the 22-year-old Stokes responded in kind, prompting umpire Marais Erasmus to step in to defuse the tension.
The session belonged to Clarke, who roughed up Panesar early and in turn carted England's seamers Stuart Broad, James Anderson and Stokes to all corners of the ground.
Clarke's ton was his second in two Tests and the 32-year-old now boasts a peerless record of two double-centuries, four tons and three 50s from his last nine matches at Adelaide Oval, with a high score of 230 against South Africa a year ago.
Clarke, who drove Australia into a dominant position with a century at the Gabba in the opening Test, brought up his 26th Test ton by working Stokes off his pads for two runs through square leg.
He tore off his helmet, kissed the insignia and raised his arms aloft in triumph as a big crowd at Adelaide Oval roared their approval.