Australia were set a target of 281 to win the first Test of a five-match Ashes series on the fourth day at Edgbaston.
England, in their second innings, were dismissed for 273, with Australia captain Pat Cummins taking 4-63 and Nathan Lyon 4-80 as the off-spinner moved to within sight of 500 Test wickets.
Several England batsmen made it into the 40s but there was no half-century in the innings, with Joe Root and Harry Brook both scoring 46.
But England’s last two wickets added 44 runs.
Only three teams have made more than 200 to win in the fourth innings of a Test at Edgbaston.
The highest chase was England’s 378-3 against India last year and the next best was South Africa’s 283-5 in 2008.
Australia are bidding for their first Ashes series win in England in 22 years, with England aiming for a first campaign triumph over their arch-rivals since 2015.
© Agence France-Presse