It came after the visitors — who must win in Melbourne — were rocked by four positive Covid cases in their camp, although no players were among them.
Australia were all out for 267, earning an 82-run lead on England’s first-innings 185 on an MCG pitch that was still offering plenty for the bowlers.
Marcus Harris top-scored with a battling 76 against a dangerous English attack led by veteran Jimmy Anderson, who was at his fearsome best with 4-33 off 23 overs.
After heavy defeats in Brisbane and Adelaide, England must win to keep the five-Test series alive, with Australia only needing a draw to retain the urn as holders.
An incredible finish to day two! Brilliant bowling from Mitch Starc and Scott Boland has our boys in a very stron… https://t.co/PHMVDMR7iM
— Cricket Australia (@CricketAus) 1640591409000
But faced with surviving the final hour against a revved-up Mitchell Starc and Pat Cummins, England collapsed again, slumping to 31 for four at the close.
Struggling opener Zak Crawley never looked comfortable and after dodging 15 balls he was caught by wicketkeeper Alex Carey for five off Starc.
Dawid Malan came in but incredibly was out first ball to Starc lbw after an unsuccessful review, then Scott Boland ruined Haseeb Hameed’s day on seven, with Carey gloving an edge.
Fired up, Boland bowled Jack Leach without scoring two balls to leave skipper Joe Root unbeaten on 12 and Ben Stokes on two — and England in deep trouble.
England earlier took their chances with the key wickets of Marnus Labuschagne (1) and Steve Smith (16), along with nightwatchman Nathan Lyon, before lunch.
England 4/31 (!!) at stumps, still trailing by 51 runs.Root (12*) and Stokes (2*) to resume tomorrow morning… https://t.co/4HSuujFp8P
— 7Cricket (@7Cricket) 1640590571000
Harris (76) and Travis Head (27) surrendered in the second session before England mopped up the rest.
Australia resumed on 61 for one with the maligned Harris, who started on 20, under pressure after a poor series so far.
But he hung on grimly as Australian wickets tumbled around him to repay the faith of coach Justin Langer by bringing up only his third 50 in 13 Tests, and his first in two years.
He then fell on 76 with the brilliant Anderson enticing an edge that Root took at slip.
Head, who made a swashbuckling 152 at the first Test in Brisbane, compiled a good-looking 27 before flailing at a probing Ollie Robinson ball, also caught by Root to snap a 60-run stand with Harris.
Play began half an hour late after Covid drama in the England camp, with the team forced to undergo urgent rapid antigen tests as they were about to leave for the MCG.
All players came back negative, but two support staff and two family members tested positive.
Coronavirus impacted the second Test at Adelaide with Australian captain Cummins ruled out just before the start for being in close contact with a positive Covid-19 case.
When play started, Lyon didn’t last, hitting 10 before prodding at a full-length Robinson delivery to Jos Buttler behind the stumps.
Harris smacked an early boundary off Anderson, but was cautious. He survived a review decision on 36 after being given out lbw and a difficult stumping on 63 before his luck finally ran out.
Labuschagne, the new number one Test batsman, had a rare failure, undone by the pace of Mark Wood, edging to Root on one in a massive moment for a resurgent England.
Harris was joined by the usually reliable Smith, who made 16 before being bowled by Anderson to leave the match finely poised.
Head also succumbed to the safe hands of Root, off Robinson, then Leach trapped Cameron Green lbw for 17.
Stokes removed Carey, also for 17, before late cameos from Cummins and Starc added valuable extra runs.