Sutherland's superb 163 boosted Australia to 5-422 at stumps on day two for a 252-run first innings lead that could already be match-winning.
Beth Mooney, filling in as wicketkeeper for Alyssa Healy, faces a nervous sleep after ending play unbeaten on 98 and closing in on her maiden Test century.
An already disastrous tour has become a nightmare for England, who are set to suffer the first 16-0 points whitewash since the multi-format Ashes was introduced in 2013.
Starting the day at 1-56, Australia toyed with England, who were their own worst enemy in dropping eight catches, missing a stumping, and being generally sloppy and listless in the field.
Sutherland was dropped twice in Friday's first session and never looked back to score her second Ashes Test century after an unbeaten 137 at Nottingham in 2023.
The 23-year-old reached her milestone just after drinks in the second session, with her family - including her father, former Cricket Australia boss James Sutherland - proudly watching from the stands.
Sutherland's 163 came off 258 balls and featured 21 fours and a six. (James Ross/AAP PHOTOS)
In just her sixth match, Sutherland has equalled Betty Wilson and Jill Kennare for the most women's Test centuries by an Australian.
Five women have scored four Test centuries, while England great Janette Brittin stands alone with five.
Sutherland is the first woman to make a Test ton at the MCG, surpassing England keeper Betty Snowball's 83* in 1935 for highest score at the venue.
With a Test average that's swelled to 83.71, Sutherland joined Karen Rolton as the only Australians to twice pass 150 in Tests.
Alyssa Healy was one of four wicket to fall as Australia dominated day two. (James Ross/AAP PHOTOS)
Sutherland, who hit her previous two Test centuries lower down the order, was promoted to No.3 after star veteran Ellyse Perry injured her hip while fielding on Thursday.
But after Perry was assessed overnight, Australia said she was available to bat in this innings if required
That remains a big if as England's morale sinks to new lows, placing significant pressure on captain Heather Knight and coach Jon Lewis.
Captain Alyssa Healy was the only wicket to fall in the second session.
She was fuming after being given out lbw and reviewed the decision, convinced she had hit the ball.
Video evidence was inconclusive, and she had to depart for 34.
Annabel Sutherland brings up her THIRD Test century at the mighty MCG where she grew up watching cricket 🥹 — Australian Women's Cricket Team � (@AusWomenCricket) Special #Ashes pic.twitter.com/4nGjhSHeR3January 31, 2025
Beaten 3-0 across the ODI and T20 series, England's performance in this Test has been somehow less competitive than in the shorter formats, where they occasionally looked capable of winning.
Quick Lauren Bell (2-94) has toiled hard across 25 overs, while star spinner Sophie Ecclestone was unlucky not to have dismissed Sutherland twice.
Maia Bouchier's drop in slips was the worst of the lot, putting down a chance that Mooney hit straight to her.
But Ecclestone (2-134) put down three chances herself.
Her efforts were in stark contrast to Australia star Alana King's leg-spin masterclass on Thursday when her 4-45 helped bowl England out for 170.
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