Joe Root was 30 not out and Jonny Bairstow one not out after Ian Bell made 53 on his Warwickshire home ground.
Earlier, James Anderson took his Ashes-best figures of six for 47 as Australia, who won the toss, were bowled out inside 37 overs.
Veteran opener Chris Rogers top-scored with 52 in an innings where no other batsman made more than Adam Voges's 16.
The five-match series is level at 1-1 after England won the first Test in Cardiff by 169 runs before Australia hit back with a 405-run victory in the second Test at Lord's.