England were bowled out for 157 in 283 minutes and heading for an expected huge defeat with seven sessions to play in forecast sunny conditions.
Ponting, keeping in mind the second Adelaide Test getting underway next Friday and the workload on his four bowlers, opted to bat again and amass an impregnable total for England to chase on a wearing pitch.
At tea on the third day on Saturday, Australia had stretched their overall lead to 478 runs at 33 without loss with Matthew Hayden on 25 with five fours and Justin Langer on seven.
Senior paceman Glenn McGrath captured his 29th five-wicket haul in Test cricket and 10th against England to finish the innings with 6-50 off 23.1 overs.
McGrath, who turns 37 next February, now has taken 548 Test wickets, the third best of all-time.
Wise-cracking McGrath made fun of pre-Test fears that he was past his best by imitating a geriatic hobbling off the field to the amusement of the crowd.
McGrath followed up the wickets of both England openers Andrew Strauss (12) and Alastair Cook (11) late Friday, to dismiss Kevin Pietersen (16), Geraint Jones (19), Steve Harmison (0) and Ashley Giles (24) on Saturday.
First-change paceman Stuart Clark took 3-21 off 14 overs and Brett Lee 1-51 off 15 overs, leaving little for master leg-spinner Shane Warne, who only bowled nine of the 61.1 overs as the pacemen thrived on the Gabba pitch.
Only Ian Bell showed significant resistance for England with a patient 50 in almost four hours.
Clark removed Bell with the second ball of a new spell when the No.3 attempted to drive only to thick-edge chest-high to Ponting at second slip.
Bell, who averaged just 17.10 in last year's Ashes series, batted for 228 minutes for his dogged half-century off 162 balls with five boundaries.
The tourists' slim chances of saving the Test nosedived after the dismissals of Pietersen and Flintoff within five balls in the first hour of play.
Pietersen did not offer a shot to a McGrath off-cutter and was adjudged leg before wicket. New Zealand umpire Billy Bowden gave Pietersen out but 'Hawkeye' video analysis suggested the ball was just missing off-stump.
Flintoff was soon following Pietersen back to the dressing room when he edged Lee to wicketkeeper Adam Gilchrist for a duck.
Pietersen had also had a life on 12 when he top-edged an attempted pull off Lee and skied to deep mid-on where Clark, running backwards, made a meal of it.
Australia batted through almost the first two days to set an apparently unbeatable target of 602 for nine declared.
Umpire Bowden will be sporting a bruise after he collected a full-blooded sweep from Jones on his left hip while he was standing at square leg just before lunch.