Shane Watson clubbed five sixes in his 103 before Australia declared on 6-369, setting England a massive victory target of 504.
England lost Alastair Cook in the first ball of their second innings - bowled by Ryan Harris - as the skipper became the first Test player to make a golden duck while celebrating his 100th match.
The tourists were 1-24 at lunch on a pitch which is cracking up significantly.
Australia lead the five-match series 2-0 and are perfectly placed in hot conditions to wrap up the series before the Boxing Day Test.
Resuming on 3-235, Australia declared after adding 134 runs in 17 overs at almost eight runs per over.
Watson had resumed on his overnight score of 29 off 66 deliveries.
The talented right-hander clubbed 103 off 108 deliveries.
It's No.3 batsman Watson's fourth hundred in a 49-Test career that has included 21 half-centuries.
Watson's second 50 came off 28 balls.
Steve Smith made 15 before George Bailey smashed an unbeaten 39 off 30 deliveries.
Bailey hit a world record-equalling 28 (4-6-2-4-6-6) off the final over of the innings bowled by Jimmy Anderson.
Watson was Australia's second century-maker of the innings after opener David Warner's 112 against an attack depleted by the foot injury to pace spearhead Stuart Broad.
Broad has been cleared of a foot fracture and is expected to bat in England's second innings but did not bowl in Australia's second innings after receiving a blow while batting on Sunday.
South Africa scored 4-414 in 2008 in Perth in the second-highest successful fourth-innings run chase in Test history. However that WACA pitch was a docile surface in comparison to the cracked strip in use for the third Ashes Test.
AUSTRALIA FIRST INNINGS 385
ENGLAND FIRST INNINGS 251
AUSTRALIA SECOND INNINGS 6(dec)-369
ENGLAND SECOND INNINGS
A COOK b Harris 0 1 1 0 0
M CARBERRY not out 8 31 18 2 0
J ROOT not out 7 29 23 1 0
Sundries (4lb 5w) 9
One wicket for 24
Fall: 0 (Cook).
Bowling: R Harris 3-0-13-1, M Johnson 3-1-7-0 (1w/5), N Lyon 1-1-0-0.
Batting time: 31 mins. Overs: 7.
Umpires: Billy Bowden (NZL), Marais Erasmus (RSA).