The tourists reached 174-6 at the close chasing a target of 311 to take a 1-0 lead in the five-Test Ashes series.
Another gripping day's cricket swung first one way and then the other, but a flurry of late wickets have given England the upper hand and they will be confident of claiming the four scalps they need on Sunday morning.
However, after four quite remarkable days, few would bet against yet another twist or two before stumps are finally pulled on a match which has rivalled the best of the epic series of 2005 for its sheer excitement.
Earlier, Ian Bell completed his 18th Test century before England were all out for 375 in their second innings.
Bell was finally dismissed for 109 and Stuart Broad 65 as Australia were set a ground-record fourth-innings target of 311 to win.
Broad, who had begun the day on 47, was the first to celebrate his milestone, reaching 50 in 125 balls, while Bell, 95 not out overnight, had to wait just a little longer to reach his century, pushing Mitchell Starc to cover.
The pair took their partnership onto 138 and the score on from an overnight 326-6 to 356-7 when Broad fell 35 minutes into the day's play, edging James Pattinson behind, and this time he did not hang around at the crease.
Bell was joined by Graeme Swann and the pair added 15 runs when Bell was next to depart, also edging to Brad Haddin off the reverse swing bowling of Mitchell Starc.