Adam Voges was 48 not out and Mitchell Starc nought not out, with England eyeing a win that would give them a 3-1 lead in the five-match series and see them regain the Ashes.
Pace-bowling all-rounder Ben Stokes had figures of five for 35 in 16 overs — his second five-wicket haul in his 15-match Test career after he took six for 99 against Australia at Sydney in January last year.
Earlier, England captain Alastair Cook declared his side’s first innings on a total of 391 for nine.
That left England with a mammoth first-innings lead of 331 after they had skittled out Australia for just 60 in 111 balls — the shortest-ever completed first innings of a Test match — on Thursday.
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.
Victory at Trent Bridge will see England regain the Ashes after they were whitewashed 5-0 in Australia in 2013/14.