David Warner (124) and Michael Clarke (113) both batted supremely for twin centuries as Australia piled up 401 for seven declared, therefore setting England a world-record target of 561.
That is 143 more than any team has ever made in the last innings to win a Test, and 20 in excess of the all-time first-class best.
In 15 overs of batting forced on them on the third evening, England got off to an awful start when Michael Carberry contrived to be bowled by Ryan Harris for a duck via a defensive shot which allowed the ball to roll back between his legs on to the base of the stumps.
Another head-in-hands moment saw Jonathan Trott flick a short ball from Mitchell Johnson straight into the hands of deep square-leg - and when Kevin Pietersen came within inches of running out captain Alastair Cook as he got off the mark with a manic single first ball, England's fretful mood was encapsulated.
In the circumstances, they did well to reach stumps in worsening light without further losses on 24 for two.
England had resumed with the ball on day three badly needing a revival to stay remotely in this match, after their calamitous collapse on Friday afternoon.
Their two early successes were self-inflicted blows by Chris Rogers and Shane Watson on a rain-interrupted morning - after which Warner and Clarke took over in a run-a-ball third-wicket stand of 158.
The tourists, especially once frontline seamers James Anderson and Stuart Broad had given their all, had no answer as Australia careered on in the sunshine.
Graeme Swann, on a pitch his opposite number Nathan Lyon had already demonstrated could help the off-spinner, and third seamer Chris Tremlett (three for 69) were especially ineffective - a worrying development for England, not just here but for four more Tests stretching in front of them.
It was not until Warner was guilty perhaps of minor complacency, having just crashed Broad back over his head for a six, that there was some temporary respite.
The left-handed opener tried to glide more runs behind on the off side, but instead edged Broad behind.
That man Broad had earlier earned himself a few more boos by striking with his first ball of the day.
It was hardly a deserving delivery, a loosener which Rogers somehow contrived to cut tamely into the hands of Carberry at point.
But Broad and Anderson did not make life easy for Australia's batsmen initially - and by the time the former was given a breather, the hosts had added only five runs in seven overs.
When Tremlett then started with a long-hop, duly pulled for four by Watson, it seemed the pressure was about to be quickly released.
Watson went for a repeat next ball and mistimed terminally, however, to present a simple catch to Broad at mid on.
Australia's number three departed with a flea in his ear from Anderson, and England predictably brought Broad straight back to try to discomfort Clarke - at the expense of Tremlett, despite a wicket in his solitary over.
Broad had expertly exploited Clarke's apparent weakness against the short ball in the first innings, but had no joy this time.
By lunch, Warner and Clarke already had the bowlers' measure - and in the first hour of an extended afternoon session, they showed no mercy.
Warner passed his century in 135 balls, having hit 11 fours, and Clarke greeted one spell from Swann by immediately hoisting him over long on for six in an over which cost 16 runs.
After Broad got Warner at last, Tremlett dug out a good delivery to have Steve Smith caught-behind for a duck.
But Clarke completed his hundred in just 115 balls before falling to Swann, up the wicket and bowled aiming over long on to give the off-spinner match figures of one for 192 at that stage.
Clarke's sixth hundred against England, and 25th in all, had nonetheless already ensured the tourists would be set an unfeasible target.
Swann would eventually also bowl George Bailey, playing for non-existent spin, but the second new ball merely provided an extra spike in the run rate as Brad Haddin (53) bagged his second 50 of the match.