At tea England were 3-87, still needing a further 361 runs to pull off a record fourth innings chase and prevent an unwanted place in history.
There's still more than two days left in the match, but a ruthless Australia are in no mood to delay celebrations, with Ryan Harris leading the charge with 2-13.
Alastair Cook (7), Ian Bell (16) and Kevin Pietersen (6) folded inside the first 14 overs, bringing an end to a dismal tour for England's most experienced run-scorers.
The trio all average over 45 in Test cricket, but less than 30 this summer - failing to score a century between them.
Captain Cook started the slide of 3-50, edging Mitchell Johnson behind to become the speed demon's 35th victim of the series.
Opener Michael Carberry (43 not out) didn't crack in the middle session, although his bat was split in two by Peter Siddle - the willow limply held together only by its sticker.
Debutant Gary Ballance is at the other end unbeaten on 7.
Australia set England a formidable target of 448 to win after Chris Rogers smashed his third Test century, and his second in consecutive matches.
Rogers, born in Sydney 36 years ago, continued his remarkable career renaissance by smashing the fastest of his three Test tons in 143 balls, ultimately falling for a career-high 119.
It finalised Rogers' standing as the top run-scorer from the back-to-back Ashes series.
However, under-pressure batsman George Bailey (46) faces an anxious wait to see if he'll stay in the side for South Africa after throwing away a golden opportunity to save his bacon with a big score.
Bailey was out hooking as he tried to hasten Australia's charge, but it's his consistent failures in first innings which has his place at No.6 under the microscope.
The ODI vice-captain did produce a magic moment however, when he held onto a spectacular one-handed grab at short-leg to dismiss Pietersen off the bowling of Harris.
Earlier, Brad Haddin departed for 28 having overtaken Adam Gilchrist's record (473) for most runs in a series from a No.7.
He also became the fourth Australian wicketkeeper to score 3000 Test runs, joining Ian Healy, Rod Marsh and Gilchrist.
Like Haddin, Rogers is 36 but in the form of his life.
The left-handed opener Rogers raised his arms to the applause of a pink-tinged crowd on Jane McGrath day at the SCG, following on from his match-winning second innings ton in Melbourne last week.
Rogers, known primarily for his dour demeanour, showed you can teach an old dog new tricks with another uncharacteristically fluent display with the bat - stroking 15 boundaries.
AUSTRALIA FIRST INNINGS 326
ENGLAND FIRST INNINGS 155
AUSTRALIA SECOND INNINGS 276
ENGLAND SECOND INNINGS
A COOK c Haddin b Johnson 7 (12)
M CARBERRY not out 43 (61)
I BELL c Warner b Harris 16 (19)
K PIETERSEN c Bailey b Harris 6 (10)
G BALLANCE not out 7 (25)
Sundries (5b 2lb 1nb) 8
Three wickets for 87
Fall: 7 (Cook), 37 (Bell), 57 (Pietersen).
Bowling: R Harris 8-4-13-2, M Johnson 5-1-30-1 (1nb), P Siddle 4-1-24-0, N Lyon 4-0-13-0.
Batting time: 93 mins. Overs: 21.
Umpires: Aleem Dar (PAK), Marais Erasmus (RSA).