Joe Root top-scored with 63, while Moeen Ali made a dashing 59 after Ian Bell's 53 on Wednesday.
Australia off-spinner Nathan Lyon took three for 36 in 13 overs, with Josh Hazlewood claiming a couple of late wickets in his three for 74.
England, after losing the toss, had bowled Australia out inside 37 overs on Wednesday, with James Anderson taking an Ashes-best six for 47.
The five-match series is level at 1-1 after England won the first Test in Cardiff by 169 runs and Australia the second at Lord's by 405 runs.