The Australians lost the wickets of retiring Justin Langer for 26 and opening partner Matthew Hayden for 33 to reach tea at 109 for two, with Ponting on 37 and Mike Hussey not out three.
The tourists lost their last six wickets for 57 to be dismissed for 291 shortly before lunch at the Sydney Cricket Ground on Wednesday.
Langer followed up his three dropped catches in his 105th and last Test with a short stay at the crease before he gloved a leg-side catch off James Anderson to wicketkeeper Chris Read.
Hayden was furious with himself when he chased after a wide Steve Harmison delivery and bottom-edged to Paul Collingwood at second slip, leaving the home side 100 for two in the 26th over.
Skipper Andrew Flintoff fought a lonely battle as the England tail crumbled around him in the morning session after resuming at 234 for four.
It was Flintoff's best knock of an indistinguished batting series with 89 coming off 195 minutes, including 11 boundaries and a six.
But England crashed, losing 3-13 in three overs inside the first hour.
Australia's pacemen Brett Lee, Glenn McGrath and Stuart Clark shared nine wickets between them, with leg-spinner Shane Warne claiming the last wicket of Monty Panesar for a duck.
Lee claimed two wickets in two balls and McGrath, playing in his 124th and last Test match, claimed his third wicket of the innings in the first hour's play.
Collingwood was dropped by Langer -- one of three dropped catches by the retiring opener in the innings -- at third slip off Lee when he was on his overnight score of 25.
Then on 27, Collingwood was squared up by McGrath and gave an outside edge to Adam Gilchrist to expose the brittle English tail.
Read survived a confident leg before wicket appeal before he was out next ball to Lee for two.
Read dabbled outside off-stump, giving Gilchrist his fourth catch of the innings.
Sajid Mahmood was out next ball, popping an easy catch off the shoulder of the bat to Hayden in the gully to put Lee on a hat-trick.
But Lee's hat-trick attempt was wide of off-stump, not obliging Steve Harmison to play a shot.
Harmison lasted 24 balls before he was lbw to Clark for two and Flintoff's second half-century of the series ended when he played extravagantly outside off-stump and was caught by Gilchrist off Clark.
Panesar, who was dropped by Langer, became Warne's only wicket of the innings when he was lbw attempting to sweep, terminating England's innings.
It was also Warne's 1,000th wicket in Test and one-day cricket combined -- 707 Test and 293 one-day international wickets.
Sri Lanka's Muttiah Muralitharan heads the list of international wicket-takers with 1,104.
McGrath finished with 3-67 off 29 overs, Lee 3-75 from 22 overs and Clark 3-62 off 24 overs.