Joe Root was 33 not out and Jonny Bairstow two not out in a match where an England victory would give them an unbeatable 3-1 lead in the five-match series and see them regain the Ashes.
Australia captain Michael Clarke insisted his team could still “save the Ashes” after a humiliating first day in the fourth Test against England at Trent Bridge on Thursday.
Stokes (5-35) intervened with three wickets for four runs as Australia faltered before tea.
However, they now face the prospect of a heavy defeat after being dismissed for their joint seventh-lowest Test score in 111 balls – the shortest first innings in Test history.
It was Broad’s 14th five-wicket haul in a test innings and was the first time an England bowler had taken five wickets before lunch on the first day of a test since Sydney Barnes, against South Africa in 1913.
Starc (nought not out) and Adam Voges (48 not out) will be the batsmen in the middle when play resumes on Saturday.
The Nottinghamshire man took eight for 15 on his home ground to wipe out the Aussies, taking his 300th Test wicket and drawing level with Fred Trueman on 307 overall scalps in the process.
Rogers and Warner both made ducks as Stuart Broad dismantled Australia for 60 all out on the first morning.
Steve Smith, the only batsman in the top four to get off the mark, went in the same opening over when Joe Root held onto a catch at third slip.
Yet England found their progress much harder-earned and did not always help themselves either, Warner dropped in the slips on 10 and 42 by Cook and then Ian Bell.
Root unfurled a couple of sumptuous cover drives as England eased past Australia’s total and he and Cook looked in complete control in a partnership of 62 until the captain, on 43, misjudged another swinging ball from Starc and was adjudged lbw.
But with Australia showing more fight with the bat second time around, England were starting to miss Anderson who was ruled out after suffering a side injury in their eight-wicket win the third Test at Edgbaston last week. The ball flew straight to Cook at first slip but he juggled the chance only for second slip Bell to grab the rebound.
That left Australia 90 runs behind England – with only three wickets remaining.
The tall left-armer produced another cracking ball to bowl Jos Buttler for 12 and Ben Stokes, on five, tickled Josh Hazlewood tamely down the leg-side to Nevill.
England banked a first-innings lead of 331 despite three wickets for five runs from Mitchell Starc on the second morning at Trent Bridge.