Australia are edging closer on a famous win after Jhye Richardson removed Chris Woakes on 44, handing England their seventh blow in the chase of 468 on Monday.
The visitors resumed the pink ball Test in deep trouble at 82 for four chasing a nominal 468 to win and needing a miracle to avoid going 2-0 down in the five-Test series.
They lost two more wickets in the opening session, with Stokes, who had scored 12, and Ollie Pope on four succumbing to relentless pressure from left-arm pace bowler Mitchell Starc and off-spinner Nathan Lyon.
At dinner in the day-night encounter, Jos Buttler was 16 not out and Chris Woakes unbeaten on 28, with England still 326 runs from victory and needing to survive two sessions with the second new ball due after just six more overs. England slumped by nine wickets in the first Test at Brisbane and if they lose this week their hopes of winning back a trophy they last secured on Australian turf in 2010-11 are all but over.
Earlier on Sunday, Joe Root fell in the final over of the fourth day to leave England in deep trouble at 82 for four.
No team has ever posted such a big score in a fourth innings to win in the history of Test cricket — with the West Indies’ 418 for seven in beating Steve Waugh’s Australia at St John’s in 2003 the highest.
It is an even harder task at the Adelaide Oval, where Australia’s 315 for six to defeat England in 1902 remains the best fourth-innings run chase.
England’s problems stem from losing seven wickets for 86 runs as they collapsed to 236 all out on Saturday in reply to Australia’s 473 for nine declared.
They reached the close with ailing skipper Root out in the last over of the day, leaving Ben Stokes unbeaten on three.
England are still 386 runs adrift, facing the near impossible task of batting three sessions on the final day to salvage a draw with only six wickets left and the world’s number one ranked Test batsman, Root, back in the pavilion.
“Any time one of your best players is out the team takes a knock but what you have to understand and believe is that the rest of the guys are going to fight as hard as he would,” England bowling coach Jon Lewis said of Root.
“They will try to survive the day tomorrow to get ourselves out of this game with a draw. It’s a big ask, I know.”
The hosts resumed their second innings at 45 for one and declared on 230 for nine before tea, giving their bowlers a crack at England with the pink ball as twilight loomed.
They immediately made inroads with Jhye Richardson steaming in to Haseeb Hameed and the ball flying off his glove to wicketkeeper Alex Carey without scoring.
Then Dawid Malan, who hit 80 in the first innings, was trapped lbw by Michael Neser for 20.
Opener Rory Burns was desperate for a big score after a lean spell and managed 34, but was then beaten by Richardson’s sheer pace, edging to Smith at slip.
Root hurt his abdomen during a warm-up and missed the opening 85 minutes while he went for a scan.
He appeared mostly untroubled while batting but late in the day took a nasty blow in the same, sensitive, area from Mitchell Starc to leave him writhing in agony.
Root gingerly got up, but in a huge blow was out for 24 in the final over, caught by Carey off Starc.
With England crashing by nine wickets in the first Test at Brisbane, their hopes are all but over of going into the Boxing Day Test at Melbourne in a week’s time only 1-0 down.
A 2-0 deficit in the five-match series will mean the Ashes are as good as gone. The only instance of a team coming from 2-0 down to win the urn was by Australia in the 1936-37 series.
“Fantastic to get out of the night session with four wickets down and a big day tomorrow,” said Australia vice-captain Travis Head.
“They’ve still got some quality players … I think Nathan Lyon will play a massive part, the ball is turning.”
Earlier, Marnus Labuschagne and Travis Head both made 51 for Australia, steadying the innings after England took three wickets for seven runs to start the day.
Marcus Harris resumed not out 21 with nightwatchman Neser on two after they lost David Warner to an amateurish run-out the previous evening.
Neser only survived seven balls before Jimmy Anderson rattled his middle stump, and Harris departed to a blinding catch from wicketkeeper Jos Buttler.
Buttler’s celebrations were short-lived when he incredibly missed a regulation catch off Smith the very next ball, in a blunder reminiscent of the two sitters he put down from Labuschagne in the first innings.
But he made amends by taking another fine diving catch to remove Smith for six off Ollie Robinson.
Head raced to an eighth Test half-century from 49 balls, but then pulled Robinson to Ben Stokes in the deep.
Labuschagne took 96 balls to reach his 50 but also holed out to Stokes, becoming part-time spinner Malan’s first Test wicket, before late cameos ahead of the declaration.