With an hour to bat before stumps, Australia lost David Warner for his second duck of the match, caught brilliantly by Ollie Pope in the gully off the bowling of Stuart Broad.
Marnus Labuschagne fell for five, caught by wicketkeeper Sam Billings off Chris Woakes, while Mark Wood had Usman Khawaja gloving a short ball to Billings for 11.
At stumps, Australia were 37-3 with Steve Smith on 17 and nightwatchman Scott Boland on three.
Australian captain Pat Cummins said his side had done well not to have lost more wickets.
“They’re the kind of night sessions you’ve got to be careful of in day-night cricket, if you get caught out with the new ball,” Cummins said.
“It was warm and humid tonight and the ball seemed to do a little bit more.
“I think it’s a pretty good effort only to be three down in really tough conditions.”
Billings, making his Test debut, was optimistic about getting a result.
“We bowled really nicely tonight, we created some opportunities, created a lot of intensity,” he said.
“They’re in front in the game, but we have a chance to really make a statement and make some inroads in the morning.”
England earlier bowled Australia out for 303 on a day when 17 wickets fell for 287 runs.
Australia are still in a commanding position and look likely to win this Test and claim a 4-0 win in the series.
Any hopes England had of salvaging anything from the Ashes realistically ended when their batting collapsed once again in the face of Australia’s relentless pace attack.
England lost four key wickets in the middle twilight session, including a horror stretch when Dawid Malan (25), Joe Root (34) and Ben Stokes (4) fell for the addition of just seven runs.
When the final session began, England again lost wickets at regular intervals and only reached 188 thanks to some late hitting from bowlers Chris Woakes (36) and Mark Wood (16).
The visitors have already lost the Ashes, down 3-0, and the batting frailties that have torpedoed their series were brutally exposed once again.
England had dismissed the hosts midway through the first session but then had a disastrous start to their innings when recalled opener Rory Burns was run out for no score with just two runs on the board.
Fellow opener Zak Crawley knocked a ball in front of him and called for a quick single, but the much-maligned Burns was slow to react and Labuschagne’s direct hit found him centimetres short of his ground.
Crawley, who scored a fine 77 in England’s second innings in Sydney, again looked assured until on 18 he got an inside edge onto his pad off Cummins and Travis Head took a sharp catch at short leg to leave England 29-2.
Skipper Root joined Malan at the crease and the pair set about trying to rebuild the England innings.
Both men looked comfortable for the most part and were scoring freely, getting great reward for their shots on the lightning-fast Bellerive Oval outfield.
However, Cummins brought himself back into the attack with immediate dividends when Malan tickled a ball down the leg side straight to wicketkeeper Alex Carey.
He then trapped Root lbw to leave England reeling at 81-4 and four runs later, Stokes slapped a short ball from Mitchell Starc to a diving Nathan Lyon at point.
Pope didn’t last long either and England’s only bright spark was Billings, who hit a breezy 29 with six boundaries before holing out on the fine leg boundary.
Cummins was the pick of the Australian attack with 4-45, while Mitchell Starc chimed in with two late wickets to take 3-53.
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