Clarke claimed his third Test century and first in Ashes cricket with 124, as Australia whittled England's innings lead down to just 38 runs after batting for almost 12 hours and 165.3 overs on the most benign of Adelaide pitches.
At Monday's close, England, batting a second time, were 59 for one with Andrew Strauss not out 31 and Ian Bell on 18 to hold an overall lead of 97 runs heading into Tuesday's fifth and final day.
Seamer Stuart Clark claimed the only wicket to fall in the 19 overs to stumps of Alastair Cook for nine in his first over, caught behind.
Yorkshire seamer Matthew Hoggard produced the best English bowling performance at Adelaide Oval for 77 years with his lionhearted 7-109 off 42 overs in Australia's first innings.
Australia in all probability have killed off England's winning chances after they batted themselves into an unbeatable position with 551 for six declared in their first innings over the first two days.
Australia are one-up in the series after a crushing 277-run victory in the first Gabba Test and are likely to head to Perth for the Dec 14-18 third Test having prevented England from cashing in on their massive first innings.
Clarke, who only returned to the Test side as a late replacement for injured all-rounder Shane Watson before the Brisbane Test, gratefully seized his opportunity with his century in 319 minutes with 10 fours.
Clarke's loose shot to Ashley Giles at short mid-wicket ended his 224-ball innings shortly after tea off Hoggard.
The 25-year-old NSW right-hander scored 56 in the first innings in Brisbane and his hundred in Adelaide to consolidate his place in the Australian side, while selection pressure builds on the under-achieving No.4 Damien Martyn.
Known as 'Pup' by his team-mates, Clarke holds the distinction of scoring a century in his first away Test, with a debut 151 against India in Bangalore in October 2004, followed by 141 in his first home Test against New Zealand in Brisbane the following month.
It has been a heart-breaking Test match for the bowlers on the flat Adelaide deck with 17 wickets falling in four days, two of them to spinners, for a total of 1,123 runs.
There was no sign of anything untoward in the pitch to suggest a clatter of wickets to change the course of the match on the final day.
Clarke shared in healthy partnerships of 98 with Adam Gilchrist (64) and 118 with Shane Warne (43) to bat Australia to safety.
Gilchrist looked to have a century for the taking after picking up the tempo when he smashed spinner Giles straight to Bell near the boundary rope.
Gilchrist, who had a below-par Ashes series last year with just 181 runs at 22.62 with a highest score of 49, was tested outside his vulnerable off-stump early but was playing his natural attacking game at the time of his dismissal.
Warne fell leg before wicket to Hoggard with one ball left to tea.
Australia lost their last three wickets for 11 runs in 12 overs after tea with Clarke, Stuart Clark (0) and Glenn McGrath (1).
It was big-hearted Hoggard's best bowling performance since his 7-61 among 12 match wickets in England's fourth Test win over South Africa in Johannesburg in January 2005.
John White has England's best bowling performance in an innings at the Adelaide Oval with 8-126 in 1929.
England 551 for 6 decl and 59 for 1 (Andrew Strauss 38, Ian Bell 18 n o; Clark 1 for 13) Vs Australia 513 all out (Ricky Ponting 142, Michael Clarke 124, Mike Hussey, Adam Gilchrist 64, Shane Warne 43; M Hoggard 7 for 109)