The Australians, whose late bid for victory comes after they trailed by 38 runs on the first innings, had 36 overs to get the runs at a rate of 4.6 an over on Tuesday.
First innings double-centurion Paul Collingwood fought a desperate rearguard to remain unbeaten on 22 as England unravelled under the brilliant leg-spin bowling of Shane Warne and injudicious shot-making.
Warne claimed 4-49 off 32 overs - 4-29 off 27 overs Tuesday - to spark the English slide, with the tourists losing their last nine wickets for 60.
England's 129 total was just five more than their lowest ever at the Adelaide Oval since their 124 in 1894-95.
Collingwood batted for 198 minutes and faced 119 balls for his stonewall innings and held out with James Anderson in a last-wicket partnership of 41 minutes and 54 balls to deny the Australians crucial overs to chase their runs.
Collingwood, who became the first England batsman to score a Test double-century in Australia for 70 years with his 206 in the first innings, was dropped on 18 by Matthew Hayden at slip off Warne nearing tea after Adam Gilchrist's gloves deflected the path of the ball.
After four days of just 17 wickets and 1,123 runs on a lifeless pitch, the match sprung to life with two compelling sessions as Warne ran the show with pinpoint accurate wrist-spin and as he finally enjoyed some assistance from the wearing Adelaide wicket.
A defeat here after controlling the Test up until the fourth day after amassing a huge 551 for six in their first innings would leave England two-down in the five Test series after losing the first Brisbane Test by 277 runs last week.
It was the start to the fifth day that England dreaded with Warne grabbing two wickets, Ian Bell run out in a horrible mix-up and skipper Andrew Flintoff out to a swoosh outside off-stump.
Warne, who was belted for 1-167 in the first innings, hit back in the morning with the wickets of opener Andrew Strauss and his Hampshire county team-mate Kevin Pietersen.
Strauss was out in dubious circumstances, caught at short leg by Mike Hussey for 34 off Warne in the 11th over of the day.
He played forward and appeared to just miss the ball but umpire Steve Bucknor gave him out to continue his dismal series of 12, 11, 14 and 34.
No.3 Bell was out for 26 in a dreadful mix-up with Collingwood and was run out at the bowler's end by a quick release from Michael Clarke to Warne, who knocked down the stumps.
Warne took special delight in taking the wicket of first-innings centurion Pietersen for two to make it game on for the fired-up Australians.
Warne flicked a prodigious leg-break that bowled the dangerous Pietersen, attempting to sweep, around his legs and collected off-stump.
Flintoff went after a Brett Lee delivery that moved off the pitch and edged to Adam Gilchrist for two, leaving his nerve-jangling side at 77 for 5.
Geraint Jones (10), Ashley Giles (0), Matthew Hoggard (4) and Steve Harmison (8) fell after lunch before Anderson helped Collingwood slow Australia's victory push.
England 551 for 6 decl and 129 all out ( A Strauss 34, Ian Bell 26, Paul Collingwood 22 n o; Warne 4 for 49, McGrath 2 for 15, Lee 2 for 35) Vs Australia 513 all out