Australia faced a target of 267 in 48 overs to win the second Ashes Test after England captain Joe Root declared his side's second innings on 258-5 at Lord's on Sunday.
England all-rounder Ben Stokes was 115 not out when Root closed the innings after lunch on the last day.
Australia are without Steve Smith. The star batsman was ruled out with a concussion suffered when he was hit by a Jofra Archer bouncer during his 92 on Saturday.
Australia lead the five-match series 1-0 after their 251-run victory in the first Test at Edgbaston last week.