Captain Ricky Ponting called a halt to the run onslaught with 23 overs left in the day after England could not dislodge the final wicket pair of Brett Lee (43) and Glenn McGrath (8) on Friday.
It was the third highest innings score at the Gabba in Test cricket and their highest against England here since 1946 when Australia scored 645.
Australia will have almost 90 minutes to bowl at the weary Englishmen, who have spent 11 and half hours and 155 overs in the field over almost two days.
Ponting topscored with 196, just short of his fifth Test double-century and Mike Hussey scored 86 and Justin Langer 82.
England captain Andrew Flintoff was by far his team's best bowler with 4-99 off 30 overs, while wayward pace spearhead Steve Harmison toiled away with 1-123 off 30 overs with six wides and one no-ball.
No team in Test cricket has lost a match after scoring 600 in the first innings.
The highest to lose was Australia's 586 at the Sydney Cricket Ground in 1894-95 when England recovered to win by 10 runs.