Broad and Ali share six wickets as Australia bowled out for 242 on day four for 169-run win.
Paceman James Anderson took six wickets to skittle Australia for a paltry 136 and put England in control on the first day of the third Test at Edgbaston.
Anderson (six for 47) was backed up by fellow quicks Stuart Broad and Steven Finn, on his Test return after a two-year absence, as a fascinating Ashes series took another twist.
Ian Bell led England’s reply of 133-3 with a half-century and by the close, forced early by rain, a rejuvenated home side had put their heavy second Test defeat at Lord’s behind them.
England lost Adam Lyth and Alastair Cook but Bell, promoted up the order on his home ground, played positively for his 53 before falling to a poor shot in trying to slog spinner Nathan Lyon to end a stand of 56 with Joe Root (30 not out).
Earlier, Australia, whose batsmen prospered at Lord’s in squaring the series after defeat in Cardiff, failed to cope with seam and swing-friendly conditions after winning the toss.
Anderson made hay with only opener Chris Rogers, passed fit after suffering dizzy spells in the last Test, offering resistance.
Rogers was eighth man out for 52 and not long after Australia were dismissed in 36.4 overs.
Anderson, who went wicketless in London, took four wickets in 19 balls after lunch to leave Australia in tatters.
Australia136 all out (Rogers 52, Anderson 6-47)
England133-3 (Bell 53, Lyon 2-3)