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England 227 (Overton 41, Lyon 4-60, Starc 3-49) and 4 for 176 (Root 67*, Starc 2-65) need another 178 runs to beat Australia 8 for 442 dec (Marsh 126*, Overton 3-105) and 138 (Anderson 5-43, Woakes 4-36)
Adelaide: England's fightback in the second Test suffered a huge blow at the end of a compelling fourth day in Adelaide.
Dawid Malan was bowled for 29 by Pat Cummins to leave the visitors 4 for 176 in their chase of 354.
That they are even that close is thanks in part to some fine lower-order batting in their first innings and an outstanding bowling display in Australia's second innings that continued in Tuesday's first session.
Australia, reduced to 53-4 overnight, were bowled out for 138, with James Anderson claiming his first five-wicket haul in this country.
He was backed up by Chris Woakes' 4-36 and some excellent catching as no home batsman managed to pass 20.
The tourists' momentum continued to build as an opening stand of 53 between Mark Stoneman and Alastair Cook brought Australian frustration and English optimism.
But both men fell tamely and James Vince played an awful stroke, leaving Joe Root and Malan to battle through an incredibly dramatic period under the lights.
Root successfully overturned being given out lbw to Nathan Lyon and was dropped by Cameron Bancroft, while both men survived Australia reviews in the space of three deliveries.
Though Malan fell 10 minutes before the close, captain Root remains on a hard-fought 67 and his continued presence gives England a small chance of pulling off something remarkable.
Still, it is more likely that Australia will complete victory on the fifth day, go 2-0 up and move to Perth knowing that the Ashes can be regained at the Waca.
Earlier, Australians were knocked over for 138 off 58 overs at tea and after leading by 215 runs on first innings pushed their lead past historical proportions at the ground.
The highest winning fourth innings at Adelaide Oval stands at six for 315 by Australia against England in 1902. England's highest run chase at the ground is 109 made in 1912.
Cook survived a confident lbw appeal off Josh Hazlewood when he was on one, but the Australians on that occasion did not seek a review and replays showed the ball hitting leg stump.
Cook was Lyon's 56th wicket this calendar year making him the leading wicket-taker in Test cricket in 2017.
England's all-time leading wicket-taker James Anderson took five for 43 -- his first five-wicket haul in Australia -- while fellow paceman Chris Woakes captured four for 36.
Usman Khawaja and Starc were joint top scorers with just 20 each in Australia's modest second innings.
England kept the Australians under pressure after they resumed the day at four for 53 .
Nightwatchman Lyon hit a couple of fours and was struck on the helmet grille by Stuart Broad before he holed out to mid-off off Anderson for 14 for Tuesday's first wicket.
Peter Handscomb, the other overnight batsman, struggled before he aimed to steer through the slips cordon only to be caught by Dawid Malan for 12 in 76 minutes and give Anderson his fourth wicket.
Tim Paine, who scored a half-century in the first innings, was dismissed for 11 top-edging a pull shot off Woakes and Craig Overton took a splendid sprawling catch running in from fine leg.
Starc launched a six over midwicket off spinner Moeen Ali before first innings centurion Marsh was cleaned up by Woakes for 19, ending a 32-run partnership with Starc.
