Australia were still 193 runs shy of making England, 2-1 up in the five-match series and pressing for an Ashes-clinching win, bat again.
Michael Clarke, the Australia captain, was nought not out and Adam Voges two not out.
All-rounder Stokes had tea figures of three for 20 in eight overs.
Earlier, Alastair Cook declared Egland's first innings on a total of 391 for nine.
Joe Root top-scored for England with 130 and Jonny Bairstow made 74 as the Yorkshire duo put on 173 for the fourth wicket.
Stuart Broad, who had wrecked Australia's first innings with a Test-best eight for 15, was 24 not out when Cook called a halt to England's reply.
Left-arm fast bowler Mitchell Starc led Australia's attack with Test-best figures of six for 111.
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