Resuming on Friday morning on 5-273 with matters evenly poised, Clarke has pushed on from 48 to 109 not out with the total on 5-389.
Clarke's 12th Test hundred in 31 matches as captain came off 175 balls and was his fourth for 2013.
Six of Clarke's 26 career centuries have come at the batting paradise that is Adelaide Oval.
The Aussie skipper and his NSW teammate Brad Haddin (57 not out) put on 116 runs for the morning session, extending their partnership to 132 for the sixth wicket on a pitch where Australia opener Chris Rogers had declared 400 would be a competitive first-innings total.
Clarke also scored a century in last month's first Ashes Test in Brisbane, which Australia won by 381 runs.
Troubled by a sore ankle earlier this week, Clarke showed his usual fine footwork against the spinners to reach his 50 off 100 deliveries with a streaky lofted drive through cover.
The skipper has struck 12 fours and faced 196 balls.
England had dropped three catches on day one, including Clarke on 18 and Haddin on five.
The tourists' fielding woes continued on Friday when Clarke was dropped on 91 by Ian Bell at short leg and was almost run out in the same play, while Haddin on 51 was caught behind off debutant Ben Stokes who overstepped the crease.
A fired-up Haddin exchanged words with 22-year-old Stokes at the end of the over as umpire Marais Erasmus stepped in with a wave of the hand to ease tensions.
England's Monty Panesar, in his first Ashes Test since 2009, has the unflattering figures of 1-98 while fellow tweaker Graeme Swann (1-91) is also nearing his century.
Rogers (72), George Bailey (53) and Shane Watson (51) scored half-centuries for Australia on day one.
Cricket Australia announced at the lunch interval that pace bowler Doug Bollinger, who has already been placed on standby for the third Test starting in Perth on December 13, will link up with the squad in Adelaide on Friday.
NSW left-armer Bollinger has played 12 Tests, the most recent of which was in Adelaide three years ago against England.
Bollinger is the Shield's leading wicket-taker this season with 17 scalps.
AUSTRALIA FIRST INNINGS
C ROGERS c Prior b Swann 72 203 167 11 0
D WARNER c Carberry b Broad 29 36 32 4 0
S WATSON c & b Anderson 51 163 119 6 1
M CLARKE not out 109 281 196 12 0
S SMITH b Panesar 6 22 17 1 0
G BAILEY c Swann b Broad 53 109 93 4 3
B HADDIN not out 57 142 100 5 2
Sundries (8b 4nb) 12
Five wickets for 389
Fall: 34 (Warner), 155 (Watson), 155 (Rogers), 174 (Smith), 257 (Bailey).
Bowling: J Anderson 26-9-75-1 (1nb), S Broad 22-3-72-2, G Swann 28-3-91-1, M Panesar 31-5-98-1, B Stokes 13-2-45-0 (3nb).
Batting time: 482 mins. Overs: 120.
Umpires: Marais Erasmus (RSA), Kumar Dharmasena (SRL).