Skipper Joe Root led a spirited English fightback to frustrate Australia and raise hopes of a miracle victory in the gripping second Ashes Test in Adelaide on Tuesday.

After three days of Australian dominance Root took up the challenge of a record run chase with a fighting unbeaten half-century as the momentum began to shift towards England, roared on by their bellowing Barmy Army supporters.

In contrast counterpart Steve Smith, who attracted criticism for not enforcing the follow-on despite a 215-run first innings lead in the day/night match, burned two reviews in the space of three balls and put down a tough catch.

At the close of an absorbing fourth day, England were 176 for four with Root unconquered on 67 and nightwatchman Chris Woakes not out five -- 178 runs from victory with six wickets in hand heading into Wednesday's final day.

The highest winning fourth innings at the Adelaide Oval is 315 for six by Australia against England in 1902.

Root had a leg before wicket decision on 32 off Nathan Lyon overturned on review, with the 'Hawk-Eye' tracker plotting that the ball would have gone over the stumps.

Australia lost their second and last review when Dawid Malan survived a lbw shout on three off Josh Hazlewood, with the ball again tracked as going over the stumps, in the 43rd over.

Adding to Smith's anxiety, he also dropped Malan on eight in a sharp one-handed attempted catch at slip off Lyon.

After the chaos of the previous night's session when Australia lost four wickets, England had a much better time under the floodlights. They only lost the wickets of James Vince and Malan and otherwise scored freely.

Vince was beaten by a pitched-up Mitchell Starc delivery, getting a big nick to Peter Handscomb at slip for 15. Malan put on 78 with Root before he was bowled by Pat Cummins for 29.

England lost openers Alastair Cook and Mark Stoneman before the dinner break.

Lyon won a successful lbw review to remove Cook (16). He shared in a 53-run opening stand with Stoneman, who was snapped up in the gully for 36.

The Australians were knocked over for 138 off 58 overs at tea but, bolstered by their 215-run innings lead, this left England with a record chase.

England's all-time leading wicket-taker James Anderson took five for 43 -- his first five-wicket haul in Australia -- while fellow paceman 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 53 for four.

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.

Handscomb struggled before he tried to steer a shot through the slips cordon, only to be caught by Malan for 12 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. Craig Overton took a sprawling catch running in from fine leg.

First innings centurion Shaun Marsh was cleaned up by Woakes for 19, before Anderson got his fifth wicket of the innings when Starc holed out to Moeen Ali for 20.

Hazlewood was the last wicket to fall, caught in the gully off Overton for three, leaving Pat Cummins not out 11.