Australia 204 (Haddin 65, Rogers 61, Anderson 4-67) and 2 for 231 (Rogers 116, Watson 83*) beat England 255 (Pietersen 71, Johnson 5-63) and 179 (Cook 51, Lyon 5-50, Johnson 3-25) by eight wickets
Scorecard and ball-by-ball details
England's matrix is broken
Jarrod Kimber's Ashes report: England's matrix is destroyed
This time last year, the thought of Australia's cricketers reaching Sydney with a 4-0 Ashes margin in their pockets seemed about as likely as that of the long discarded Chris Rogers making a century in the Boxing Day Test. So there was rare joy experienced by Australia, Rogers and another bounteous MCG crowd as both events came to pass, with the considerable assistance of a staggeringly listless England.
A successful chase offered vindication to Michael Clarke, who sent England in to bat in the knowledge that the drop-in pitch would improve across the match. A first Test century in Australia provided rich satisfaction for Rogers, plus the assurance that he will be on the plane for next year's South Africa tour. But another day of humiliation left England in a state of total despair, having coughed up their fourth defeat from a day three position that had looked close to impregnable.
The wretchedness of England's display was total, from dropped catches and misfields to Alastair Cook's increasingly leaden tactics. The touring bowlers, so often betrayed by their batsmen in this series, lost progressively more vigour as the target neared, allowing Rogers and a free-swinging Shane Watson to take far too many liberties. Few touring teams to Australia can possibly have put in two worse days of a Test than these.
Australia still required 201 when the day began, but Cook's men effectively surrendered the match with a pair of missed chances early in the morning session. By the time Ben Stokes struck to remove David Warner, English shoulders had slumped in anticipation of defeat, and they would slouch ever further as Rogers and Watson rolled up the target with plenty of flair in the best batting conditions of the match.
Rogers perished with 30 still to get, but even that dismissal had a silver lining. Clarke was able to walk to the wicket and collect his 8000th Test run, earning warm applause before ending the match in the company of Watson. The unbeaten and sometime estranged pair embraced warmly at the moment of victory, another scenario few would have been game to predict a year ago.
Resuming at 0 for 30, Warner and Rogers began ticking down the required runs, but would offer England a pair of chances to gain a foothold. Befitting of their play the day before, the tourists spurned them with all the disdain of a team that has lost all confidence or sense of how to grasp a match.
On 19, Rogers edged a fine delivery from Stuart Broad moving across him, and watched helplessly as the edge flew towards the slips cordon. Though it was well within reach of Jonny Bairstow, England's gloveman did not move, and Broad cursed his misfortune as the ball scuttled away to the boundary. Rogers only enhanced his feeling of injustice by upper cutting the next ball for four over the cordon.
Stokes replaced Broad after only two overs, and duly created his own chance when Warner drove at a delivery not quite there for the stroke. This time the ball travelled straight to Cook at an ideal height. When that chance went down, no-one quite knew where to look. A few overs later Warner did fall, a square slash attempt settling into Bairstow's gloves, but the muted nature of England's celebration indicated a team aware their moment may have passed.
Rogers meanwhile carried on in a manner so infuriating to bowlers, one inside edge past the stumps further cruel and unusual punishment for Stokes. There were other more fluent shots from there, however, as Rogers moved to his second half century of a low-scoring match. Watson joined in with a few sweet blows, and their partnership was soon motoring along.
As if transfixed by his own error, Cook seemed even slower to react than usual, and furrowed many brows at the ground by opting for Joe Root before Monty Panesar. Rogers was not perturbed by either, but shortly after lunch did offer another half chance - Bairstow diving over a low edge that bounced fractionally after passing under his glove.
The rest was a procession. Accompanied by Barmy Army songs that sounded evermore like gallows humour this series, Rogers and Watson unfurled numerous smart strokes, not least the punch through the off side that took Rogers to his hundred. He celebrated with a raised bat, a beaming smile and perhaps the shot of the match, cuffing Tim Bresnan through point in the next over to split Cook's attempt at a restrictive field.
Panesar eventually defeated Rogers, procuring a thin edge to Bairstow from an attempted back foot forcing stroke. But it was the merest bump on Australia's passage to victory, which Watson secured with a mow through the leg side and a fist raised in triumph. It was a win for Australia to savour, a defeat to mortify England.

Daniel Brettig is an assistant editor at ESPNcricinfo. He tweets here