At lunch on day three of the fifth Test, Australia were 7-248 and leading by an imposing 419 runs.
England now require a world record run-chase to prevent their unwanted place in history, needing to eclipse the mark of 7-418 set by the West Indies against Australia in 2003 as the highest ever successful fourth-innings total.
The highest at the SCG was 2-288 by Australia against South Africa in 2006.
Australia lost three wickets in the opening session, but Rogers, born in Sydney 36 years ago, continued his remarkable career renaissance by smashing the fastest of his three Test tons in 143 balls.
The veteran left-hander is 114 not out and will finish 10 straight Tests against England as the top run-scorer from either team.
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 towards a declaration, but it's his consistent failures in first innings which has his place at No.6 under the microscope.
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 Rogers, Haddin is 36 but in the form of his life.
Selectors took a gamble by reinstating the two elder statesmen for last year's series in the UK.
Haddin, with the exception of one Test in India as an injury replacement for Matt Wade, had spent over a year out of the Test side before earning a recall.
Rogers thought a one-off appearance against India in 2008 was the first and last Test of his career.
The left-handed opener 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 14 boundaries.
However, there were nervous moments in the 90s facing part-time offspinner Kevin Pietersen, bringing back memories of his debut ton at Durham when he spent 30 minutes stuck on 96 against Graeme Swann.
Pietersen was thrown the ball for the first time since 2012 ahead of first-choice spinner Scott Borthwick, who ultimately dismissed Haddin.
James Anderson, Stuart Broad and Ben Stokes have taken two wickets each.
AUSTRALIA FIRST INNINGS 326
ENGLAND FIRST INNINGS 155
AUSTRALIA SECOND INNINGS
C ROGERS not out 114 (163)
D WARNER lbw Anderson 16 (20)
S WATSON c Bairstow b Anderson 9 (9)
M CLARKE c Bairstow b Broad 6 (18)
S SMITH c Cook b Stokes 7 (12)
G BAILEY c Borthwick b Broad 46 (74)
B HADDIN b Borthwick 28 (40)
M JOHNSON b Stokes 4 (3)
R HARRIS not out 1 (5)
Sundries (13lb 2w 2nb) 17
Seven wickets for 248
Fall: 27 (Warner), 47 (Watson), 72 (Clarke), 91 (Smith), 200 (Bailey), 239 (Haddin), 244 (Johnson).
Bowling: J Anderson 15-6-46-2, S Broad 14-1-57-2 (1w 2nb), B Rankin 10-0-37-0, B Stokes 10-0-62-2 (1w), S Borthwick 4-0-16-1, K Pietersen 4-1-17-0.
Batting time: 265 mins. Overs: 57.
Umpires: Aleem Dar (PAK), Marais Erasmus (RSA).