After Jacob Bethell's maiden first-class century put England back in the match on day four, Mitchell Starc finally had him caught behind for 154 on Thursday.
Starc (3-72) also had Josh Tongue caught at mid-off, making it 31 wickets for the series at 19.93.
Bethell's innings will go down as one of the few highlights of the summer for England, with the 22-year-old offering reason to believe they have unearthed a star.
But for now the tourists require one of their best bowling performances of the series to avoid a 4-1 series loss that will likely have long-term recriminations to the team's hierarchy.
There are signs of inconsistent bounce and turn on the SCG wicket, but England's bowling was particularly poor as the hosts amassed 567 in their first innings.
Six fourth-innings totals of less than 200 have been defended before at the SCG, but only two of those have come in the past 50 years.
Included in that number are Pakistan's capitulation against Australia in 2010, and the hosts' famous failure to chase down 117 against South Africa in 1994.
The target could give some chance for Usman Khawaja to have one last farewell innings, requiring 13 more runs to overtake Mike Hussey and go 14th overall for Australia.
Khawaja led Australia out on to the SCG on Thursday morning, after a pre-play presentation with Glenn McGrath.
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