Needing to pull off the greatest fourth-innings chase in Test history to stay in the series, the tourists have already lost the out-of-sorts Ben Duckett and Ollie Pope.
Joe Root (37 not out) and Zak Crawley (36no) remain at the crease at tea on day four, with the latter soaking up 80 balls in a move away from his normal attacking style.
After Australia lost 6-76 on Saturday morning to be bowled out for 349 and leave the door ever so slightly ajar for England in Adelaide, Cummins did the early damage.
In a tricky two-over period before lunch, Cummins had Duckett second ball when the left-hander dabbed at a delivery outside off stump and was caught at slip by Marnus Labuschagne for four.
The opener's dismissal summed up a horror tour for the left-hander, who is yet to pass 30 and has quickly been exposed by his refusal to leave the ball.
Pope is having a worse tour, with his misery compounded by a superb one-handed grab by Labuschagne at slip after an edge off Cummins (2-19).
The England No.3's 17 on Saturday took his career average against Australia to 17.62 from eight Tests.
Root and Crawley have since added 75 for the third wicket, attempting to put the pressure back on Nathan Lyon on a turning wicket.
Realistically, though, England require a miracle.
The West Indies' 418 against Australia in 2003 the highest fourth-innings chase, while England's best effort is 378 against India in 2022.
If Australia were to win on Saturday and take a 3-0 series lead it would mark the fastest an Ashes series has been decided since 1921, with just 10 days played.
With the potential of a historic day at Adelaide Oval, Travis Head began the morning on 142 and Alex Carey 52.
Again, England were guilty of making it easy for Head, feeding him outside off stump and playing with one slip, no gully and a deep backward point.
He brought up 150 when he cut Brydon Carse to the third-man boundary for four, before two thunderous blows off the quick through midwicket and cover point.
But with a maiden Test double-century in sight, Head was out when he pulled Josh Tongue (4-70) to Crawley at deep backward square on 170.
Carey also looked on track for his second hundred of the match and become the first Australian wicketkeeper to record two tons in a Test.
After beginning his day with a cut shot for four off Carse (3-80), his wicket came out of nowhere when he nudged Ben Stokes to leg slip on 72.
Josh Inglis came and went for 10 when caught at slip, no doubt prompting consternation over whether he is squeezed out for Usman Khawaja to stay on Boxing Day.
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