The Australians batted themselves to within 49 runs of England's first innings 551 for six declared by tea on the fourth day with a draw looking increasingly likely over the remaining four sessions of play.
At tea on Monday, Australia were 502 for seven with Clarke unconquered on 121 off 215 balls, and Warne out in the last over before the interval for 43.
Only 12 wickets have fallen for a total of 1,053 runs on one of the most benign of Adelaide pitches and there was no sign of anything untoward in the wicket to suggest a clatter of wickets to change the course of the match.
Warne joined Adam Gilchrist (64) as the only Australian wickets to fall Monday with England guilty of not varying their tactics to force Australia's hand.
Warne gave Matthew Hoggard his fifth wicket of the innings when he was leg before wicket with one ball left to tea.
Clarke, who only returned to the Test side as a late replacement for injured all-rounder Shane Watson before the first Brisbane Test, batted confidently for his third Test century and first against England.
The 25-year-old NSW right-hander has seized his opportunity with 56 in the first innings in Brisbane and his unbeaten hundred in Adelaide, 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.
He played a total of 20 Tests, including all of last year's Ashes series, before he was dropped after scores of 5, 14 and 5 in the first two Tests against the West Indies in the last Australian summer.
Clarke was recalled for two Tests in Bangladesh last April before his late call-up for this series first Gabba Test.
Gilchrist looked to have a century for the taking after picking up the tempo when he smashed spinner Ashley Giles straight to Ian Bell near the boundary rope some 40 minutes before lunch.
Gilchrist clubbed eight boundaries off 79 balls and put on 98 runs with Clarke for the the sixth wicket in 112 minutes.
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 by England pacemen Matthew Hoggard and Andrew Flintoff, but survived the initial examination.
England enjoyed great success bowling to a plan against Gilchrist in 2005, exposing a weakness playing outside off-stump and restricting the free-hitting wicketkeeper-bastman from playing his natural game.