Joe Root (91), Jonny Bairstow (78) and Zak Crawley (73) were the major contributors for the hosts who trail 2-1 in the series and are battling to stop Australia winning the Ashes in England for the first time since 2001.
Crawley set the tone by driving the first ball of the day from Mitchell Starc to the cover boundary before he and Ben Duckett shared a fluent opening partnership of 79.
Duckett fell for 42 when he edged Starc to wicketkeeper Alex Carey and the Australians successfully reviewed the umpire's decision of not out but that was the touring side's only success of the morning as they struggled to restrict the flow of runs.
Crawley, who struck nine fours, was out straight after lunch flashing at a wide ball from Pat Cummins and edging a catch to Steve Smith in the slips.
Root joined Ben Stokes and they added 63 for the third wicket before Stokes (42) tried to loft spinner Todd Murphy over long on and gave Cummins a simple catch.
Root looked in excellent touch, hitting 11 fours and one six as he passed fifty for the 90th time in tests.
Harry Brook, who struck his second ball from Murphy straight for six, was dismissed for seven by a fine lifting ball from Josh Hazlewood which he nicked through to Carey.
Root looked certain to make a century but fell nine runs short, deceived by a turning delivery from Murphy that kept low and bowled him.
Bairstow also showed great attacking intent and found the boundary 11 times before playing a lazy cut at Starc and giving Carey another simple catch.
Chris Woakes and Mark Wood were out cheaply but Stuart Broad and James Anderson survived the last few overs and England will have the option of trying to extend their healthy lead before beginning the task of bowling Australia out on day four.
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