Glenn McGrath caught Steve Harmison at fine leg off Stuart Clark to end England's resistance and give the Australians a morale-boosting 1-0 lead over the holders in the five-Test series.
Clark finished with 4-72 off 24.1 overs and leg-spinner Shane Warne, who did not take a wicket on the final day, closed with 4-124 off 34 overs.
England's remote hopes of batting out the final day nosedived in the day's opening over when Kevin Pietersen was out on the fourth ball to Brett Lee.
Pietersen, who buoyed England with his counter-attacking innings, went the same way as his batting partner Paul Collingwood (96) by getting out in the nineties.
Lee took the second new ball for his second delivery and had Pietersen out to a poor shot to Damien Martyn at short mid-wicket, with no addition to his overnight score of 92.
Pietersen, who had an absorbing duel with his Hampshire county team-mate Shane Warne on Sunday's fourth day, was upset to be dismissed so softly as he fell to a half-volley from Lee.
He batted for 228 minutes with 14 boundaries and with him went the last remaining recognised batsman in England's against-the-odds bid to avoid a heavy defeat in the first of the five-Test series.
Wicketkeeper Geraint Jones, selected ahead of Chris Read primarily for his batting, went 30 minutes later when he chopped a Glen McGrath ball on to his stumps for 33 after hitting five fours in his 68-minute stay.
Ashley Giles, also chosen ahead of Monty Panesar for his batting ability, was out at first-hour drinks when he edged Clark to Warne at first slip for 23, leaving the tourists at 346 for eight.
Matthew Hoggard followed when he edged Clark to Warne at slip for eight and Harmison was the last man out, hooking to McGrath off Clark.
England had needed to defy history to get anywhere near Australia's huge lead with their highest successful fourth-innings run chase in an Ashes Test 332 for 7 in Melbourne in 1928.
England will be looking to regroup for Friday's second Adelaide Test after being dominated for the opening three days here.
Man-of-the-match and captain Ricky Ponting received criticism from local pundits for not enforcing the follow-on after Australia held a 445-run innings lead after dismissing the tourists for 157.
Ponting and McGrath took the field on the final day after treatment overnight for injuries which kept them off the field during Sunday's play.
Ponting strained his upper back while turning for a run during his 24 minutes of batting early Sunday while McGrath required a pain-killing injection to his left heel.
Team physiotherapist Alex Kountouris believes the pair will overcome their problems in time to play in Adelaide.
Australia 602/9 decl and 202/1 decl beat England 157 and 370 (Paul Collingwood 96, Kevin Peitersen 92, G Jones 33; Stuart Clark 4 for 72, Shane Warne 4 for 124)