The home side will resume on day four on Sunday at the MCG on 0-30, requiring a further 201 for victory on a two-paced MCG pitch that has yielded scores of 255, 204 and 179.
Eleven wickets fell on a windy day three in front of a noisy crowd of over 63,000.
If Australia win it would be the ninth-highest successful Test run chase at the MCG and the highest since December 1962.
No Test team has successfully chased a target of over 200 at the MCG in three decades. Drop-in pitches have been used for Tests at the venue since December 2000.
Spinner Nathan Lyon joined the 100-club with a five-wicket haul as England were bowled out for 179 in their second innings.
While tearaway quick Mitchell Johnson grabbed 3-25 off 15 overs to surge to 31 victims for the series and eight for the match, it was Lyon who grabbed centre stage in front of over 63,000 fans at the MCG.
The 26-year-old offspinner claimed 5-50 and moved to second on the series wicket-taking list for Australia with 16.
England lost their last five wickets for six runs as Lyon pounced, with Kevin Pietersen his most important victim for 49.
After an opening stand of 65 highlighted by skipper Alastair Cook's breezy 51, England lost 4-22.
Cook was lbw to Johnson and fellow opener Michael Carberry (12 off 81 balls) fell in the same fashion to Peter Siddle at 2-86 in the 28th over.
Player-of-the series contender Johnson claimed two wickets as a fielder in the next over, bowled by Lyon.
Johnson threw down the stumps at the bowler's end to run out Joe Root and two deliveries later Ian Bell was caught by Johnson at mid off for a golden duck at 4-87.
Lyon's heroics included dismissing tailenders Tim Bresnan and Stuart Broad for ducks with the score on 174 to become the 35th Australian to claim 100 Test wickets.
Pietersen holed out to long off from Lyon's bowling and Monty Panesar was lbw to Johnson.
Johnson had a verbal clash with Pietersen, who pulled away several times while the bowler was running in. Johnson at one stage threw the ball towards the batsman in frustration.
Australia resumed on 9-164 and were bowled out for 204, a first-innings deficit of 51.
Brad Haddin top-scored with a gusty knock of 65 and added 40 valuable runs for the last wicket with Lyon.
ENGLAND FIRST INNINGS 255
AUSTRALIA FIRST INNINGS
C ROGERS c Pietersen b Bresnan 61 (171)
D WARNER c Bairstow b Anderson 9 (14)
S WATSON c Bairstow b Stokes 10 (15)
M CLARKE b Anderson 10 (34)
S SMITH c Bell b Broad 19 (77)
G BAILEY c Bairstow b Anderson 0 (19)
B HADDIN c Bairstow b Anderson 65 (68)
M JOHNSON c Anderson b Bresnan 2 (30)
R HARRIS c Root b Broad 6 (27)
P SIDDLE c Bresnan b Broad 0 (5)
N LYON not out 18 (34)
Sundries (4lb) 4
Fall: 19 (Warner), 36 (Watson), 62 (Clarke), 110 (Smith), 112 (Rogers), 122 (Bailey), 151 (Johnson), 162 (Harris), 164 (Siddle), 204 (Haddin).
Bowling: J Anderson 20.2-4-67-4, S Broad 20-6-45-3, B Stokes 15-4-46-1, T Bresnan 18-6-24-2, M Panesar 9-2-18-0.
Batting time: 370 mins. Overs: 82.2.
ENGLAND SECOND INNINGS
A COOK lbw Johnson 51 (64)
M CARBERRY lbw Siddle 12 (81)
J ROOT run out (Johnson) 15 (24)
K PIETERSEN c Harris b Lyon 49 (90)
I BELL c Johnson b Lyon 0 (1)
B STOKES c Smith b Lyon 19 (55)
J BAIRSTOW c Haddin b Johnson 21 (28)
T BRESNAN b Lyon 0 (8)
S BROAD c Clarke b Lyon 0 (3)
J ANDERSON not out 1 (6)
M PANESAR lbw Johnson 0 (6)
Sundries (5b 6lb) 11
Fall: 65 (Cook), 86 (Carberry), 86 (Root), 87 (Bell), 131 (Stokes), 173 (Bairstow), 174 (Bresnan), 174 (Broad), 179 (Pietersen), 179 (Panesar).
Bowling: R Harris 10-1-34-0, M Johnson 15-5-25-3, N Lyon 17-3-50-5, P Siddle 15-6-46-1, S Watson 4-2-13-0.
Batting time: 287 mins. Overs: 61.
AUSTRALIA SECOND INNINGS
C ROGERS not out 18 (29)
D WARNER not out 12 (19)
No wickets for 30
Bowling: J Anderson 3-1-5-0, S Broad 3-0-16-0, M Panesar 1-0-4-0, B Stokes 1-0-5-0.
Batting time: 36 mins. Overs: 8.
Umpires: Aleem Dar (PAK), Kumar Dharmasena (SRL).