The fourth day was washed out by rain and Australia, 3-0 down in the series, needed early wickets to retain a chance of a consolation victory.
They did dismiss Chris Woakes for 25, Ian Bell (45) and Stuart Broad (nine) but Matt Prior made 35 not out and Graeme Swann a breezy unbeaten 24 off just 11 balls to leave England 142 runs behind with two sessions left.
The hosts resumed on 247 for four and Woakes soon edged a good-length ball from Ryan Harris straight to Michael Clarke at second slip.
Prior, searching for form after a disappointing series with the bat, played positively from the start.
He pulled Harris for four and clipped Peter Siddle through mid-wicket for two to take England to their follow-on target of 293.
Bell had continued his rich vein of form and his dismissal was unlucky when he flicked James Faulkner down the leg-side and was well caught by wicketkeeper Brad Haddin.
Bell, Faulkner's first test victim, has scored 545 runs in the series and made three centuries.
Prior's fifth four, a slash to third man off Siddle, took England past 300 but Mitchell Starc returned to the attack to uproot Broad's middle stump.
Swann immediately went on the offensive, taking 10 runs off the first three balls he faced from Starc and dancing down the pitch to hit off-spinner Nathan Lyon straight for six at the end of an entertaining session.