England, who have already lost the series, trail the hosts by 210 runs and with only six wickets in hand, face a tough task of avoiding a 0-4 defeat.
Resuming the day at 479/4, both Shaun, overnight on 98, and Mitchell, overnight on 63, went on to register their second centuries of the series, adding 169 for the fifth wicket.
After declaring their first innings at 649/7, Steven Smith-led Australia took a 303-run first-innings lead at the Sydney Cricket Ground.
Shaun was the first to get to his three-figure mark, adding the two runs required to bring up his sixth Test hundred. He drove spinner Moeen Ali through the covers in just the fifth ball of the day to bring up the mark.
England soon took the third new ball, but the brothers, happily settled in now, weren't to be denied their rare opportunity to meet as unbeaten Ashes centurions mid-pitch.
Seamer Stuart Broad was hit for consecutive fours by Mitchell in his first two overs of the day. That fourth boundary took him up to 99, and the ran for a double off Tom Curran to complete the 100.
Mitchell let his guard fall, and was dismissed next ball when Curran jagged one back in. Tim Paine and joined Shaun, and the two then added a quick 52, the latter putting away boundaries almost every over.
His stand eventually came to an end, run out after Paine called him for a quick single. Starc followed suit after a quick 11, and Smith called his wards back in after Paine and Cummins added a brisk unbroken 52.
England, trailing by 303 runs, couldn't get it going. Mark Stoneman (0) was trapped in frontof the wicket by Mitchell Starc in the third over the third over.
The partnership between Alastair Cook (10) and James Vince (18) then lasted just 17 deliveries before Cook was trapped lbw by spinner Nathan Lyon, while Vince ran out of luck after edging paceman Pat Cummins to Steve Smith at slips.
Captain Joe Root (42 batting) then came in and held up one end. He added 25 with Dawid Malan (5), who was dismissed by a lbw verdict in favour of Lyon.
Jonny Bairstow (17 batting) gave Root company till the end of the day.
Brief Scores: England first innings: 346 and 93/4 (Joe Root 42 batting; Nathan Lyon 2/31) vs Australia first innings: 649/7 declared (Usman Khawaja 171, Shaun Marsh 156, Mitchell Marsh 101, Steve Smith 83; Moeen Ali 2/170) on Day 4.
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