Chris Rogers completed his second century in successive Tests as Australia set England a world-record 448 to win at the SCG.
As well as needing a new all-time Test best in the fourth innings, the tourists must therefore also exceed their highest total of a sorry series by 95 runs if they are to escape an Ashes whitewash.
Rogers took the respective century count this winter to an astonishing 10-1 in Australia's favour when he cut part-time off-spinner Kevin Pietersen for his 14th four.
George Bailey fell four short of a second Test half-century, in a fifth-wicket stand of 109 with Rogers which helped the hosts to 276 all out by early afternoon on day three.
Bailey's departure, caught at deep square-leg off Stuart Broad, gave Brad Haddin an opportunity to try to pass 50 for the seventh time in the series.
He soon made it clear he was in a hurry to do so as well.
Haddin's eyes lit up a little too much when he spotted a Scott Borthwick full toss, though, and he under-edged the slog-sweep to be bowled off-stump and fall seven runs short of a 500 series aggregate.
Mitchell Johnson was then bowled round his legs, trying to manufacture another scoring opportunity off Ben Stokes, and after lunch Rogers chipped a catch back to Borthwick (three for 33) to go for a career-best 119.
The young leg-spinner also had Ryan Harris caught at deep midwicket, and finally Boyd Rankin got his maiden Test wicket when Peter Siddle attempted to hook a bouncer but was caught behind to be last out.