Joe Root took it upon himself to keep English hopes alive as his team tried to complete a remarkable reversal of fortune in the second Ashes Test at the Adelaide Oval.

Root's men earned an outside shot at a national-record run chase after bowling Australia out for 138 and then reaching 176-4 by stumps on day four, on the back of their captain's unbeaten 67, in pursuit of a highly-improbable 354.

The architects of England's improvements, dating back more than 24 hours after their miserable start to this match, have been Chris Woakes and Craig Overton with the bat and then James Anderson and Woakes again with the ball.

Anderson recorded his first five-wicket haul in Australia, while Woakes finished with four for 36, as the hosts mustered only a joint top individual score of 20 after Steve Smith chose not to enforce the follow-on the previous evening.

Then Root ensured England would take it into the last day here to determine whether they will go to Perth level again at 1-1 or a dispiriting 2-0 down with three to play.

England's second-innings efforts with the ball were outstanding, as was their fielding.

Stuart Broad intimidated Nathan Lyon early on, and Anderson reaped the reward when the nightwatchman holed out to mid-off.

In his next over, Anderson (five for 43) had an out-of-sorts Peter Handscomb especially well-held by Dawid Malan diving to his right at gully.

And Woakes got in on the act thanks to an even better catch of contrasting style when Overton made ground from fine-leg to cling on as he threw himself forward following a mis-hook by Tim Paine.

Mitchell Starc and Shaun Marsh gave the hosts some significant extra leeway until Woakes bowled the first-innings centurion as he aimed to leg.

Starc then became Anderson's fifth victim, miscuing to deep mid-off, and Overton finished the job when Josh Hazlewood propped a catch to gully.

England had given themselves the slimmest of unexpected chances, and their top order was never going to lack for motivation after its collective first-innings mishap.

But the odds, and around 140 years of Ashes history, were still stacked ominously against them.

A half-century opening stand raised hopes, Alastair Cook surviving on one when Australia incorrectly chose not to review for a Hazlewood lbw.

But Cook, lbw to Lyon after Smith did go to DRS this time, and then Mark Stoneman - propping Starc to gully - were to go for the addition of only a single.

Vince began the dangerous dusk-and-dark session by edging a drive at Starc to slip, leaving the onus more than ever on Root.

He needed some fine-margin decisions to go his way, notably when he reviewed an lbw decision against him off Lyon on 32 and saw technology demonstrate the ball clearing middle-stump by a whisker.

He also survived on 60 when Cameron Bancroft could not hold a sharp chance at short cover off Pat Cummins.

But there was decidedly more skill than luck about Root's hugely-determined 78-ball half-century as he and Malan battled through 26 overs together under lights until the left-hander was bowled by a beauty from Cummins just before the close.