In reply to Australia's second innings score of 369 for six declared, the English put up a valiant fight but were bowled out for 353.
Bowler of the series Mitchell Johnson fired a delivery into the rib cage of his rival fast bowler James Anderson, who was powerless to do anything other than offering a simple catch to George Bailey at short leg.
As the on-field celebrations began, vice-captain Brad Haddin embraced Clarke and shouted "We've got them back".
"It was a tough night's sleep last night for a lot of the boys," Clarke said shortly after the final wicket was taken.
"But our goal is to get back to being the No.1 team in the world. So we'll celebrate tonight, we deserve that, but then we get back to hard work because there's two more Test matches to play in this series."
Having waited four years, three months and 25 days to regain the tiny terracotta urn, a few more hours should have been a matter of little consequence.
But the Australians would not have enjoyed their lunch after their full bowling complement, armed with both a very old and then a brand new ball, was able to capture a solitary England wicket after 29 overs of toil.
Those who had bravely called the result foregone at the close of day four or earlier were also shifting restlessly in their seats.
The arrival of young all-rounder Ben Stokes galvanised the tourists' spirit to the point that after Kevin Pietersen's dismissal -- cited by many as the end of England's hopes -- Monday evening the next three wickets added 215 runs on a pitch that was supposed to be diabolical for batting.
Having failed to make an early breakthrough on the final morning, the Australians pinned their hopes of an early celebration on the second new ball which became due after an hour's play.
However, Stokes and Matt Prior (26) refused to buckle and remained bravely undaunted by the sight of occasional deliveries skewing sideways off the widening and deepening cracks in the WACA pitch.
The breaking point finally came when Prior flashed at a delivery, more of an instinctive pressure release than a moment of weakness, and edged a catch to Brad Haddin.
If the door had opened briefly for the Australians, Stokes and fellow all-rounder Tim Bresnan (12) used every tool in their armoury to prevent it swinging further.
Stokes, who spent a nervous 44 minutes in the 90s in search of his first Test century in just his second match, finally found some fluency against Johnson and helped himself to 12 runs off a single over that carried him to three figures.
As the first England player to notch the milestone in this series, Stokes remains the single positive to emerge from the campaign to date and showed enough in the space of two matches to suggest he has a significant future at the top level.
But when he fell in the third over after the lunch break, attempting to remain positive by trying to sweep Nathan Lyon having scored a match-high 120 in very trying conditions, England's resistance quickly crumbled.
The final four wickets fell in the space of 7.2 overs and just 35 minutes after the lunch break and the Australian celebrations began.
Australia: 385 all out (Steven Smith 111, David Warner 60; Stuart Broad 3/100) and 369/6 declared (David Warner 112, Shane Watson 103; Tim Bresnan 2/53, Ben Stokes 2/82).
England: 251 all out (Alastair Cook 72, Michael Carberry 43; Ryan Harris 3/48, Peter Siddle 3/36) and 353 all out (Ben Stokes 120, Ian Bell 60; Mitchell Johnson 4/78, Nathan Lyon 3/70).
--IANS (Posted on 17-12-2013)