With four sessions still to play England were 180 for two in their second innings on Sunday, still needing another 377 for an incredible win.
Opener Alastair Cook was not out on 80 with Paul Collingwood on four, the tourists showing plenty of fight by losing just one wicket in the first two sessions of the penultimate day.
Australia are already 2-0 up in the five-Test series and victory in Perth would see them regain the Ashes they lost in 2005.
Apart from overhauling the huge target, England's only other hope is to bat out the match for a draw that would at least keep the series alive.
England resumed at 19 for one with overnight batsmen Ian Bell and Cook boosting the tourists' spirits by defying the Australian attack for more than 50 overs on another hot day.
Cook and Bell added 170 for the second wicket before Bell was denied a well-deserved century when he became Shane Warne's 696th Test wicket from the last ball of the 51st over of the day.
Bell had batted with a perfect mixture of patience and strokeplay to frustrate the Australians, but got under a fullish delivery from Warne and drove it straight to Justin Langer at short mid-off.
He had been at the crease for 234 minutes, faced 163 balls and hit eight fours and two sixes.
Bell generally played Warne well, using his feet when appropriate and twice lofting the leg-spinner straight down the ground for six.
He did enjoy a life on 73 when wicketkeeper Adam Gilchrist grassed a catch off the bowling of Brett Lee.
The left-handed Cook, a promising player who has produced his first significant innings of the series, was generally more circumspect.
He endeavoured to leave the balls just outside his off stump that have been his downfall this series, although at times his concentration appeared to waver.
There was little assistance from the wicket for Australia's fast bowling trio of Lee, Glenn McGrath and Stuart Clark, with just the odd ball climbing more than expected off the pitch.
However, Warne extracted plenty of turn as he bowled unchanged from the northern end between lunch and tea.