England need four wickets for victory and Australia 137 runs as the first Test heads into a potentially thrilling fifth day at Trent Bridge.
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.
Swann was the next to go for nine, edging to Michael Clarke at first slip to give Peter Siddle this first wicket of the day.
Siddle then got his second - and his eighth of the match - when last man James Anderson mis-timed a drive to Phil Hughes two balls later.
In reply, openers Shane Watson and Chris Rogers brought Australia's target below 230 runs with an 84-run partnership.
The pair hit 28 in the seven overs before lunch and then pushed on in positive style following the interval before Broad captured Watson leg before for 46.
Just a run later, Rogers was given out caught behind from a Swann delivery but a successful review proved he had not touched the ball and he progressed to his half-century at tea.
Ed Cowan moved on to 14, with Australia on 111-1 and back in control, before Jonathan Trott caught him off Joe Root right on the stroke of tea, in the latest twist of this ebb-and-flow game which prompted exuberant celebrations from part-time spinner Root at his first Test wicket.
Australia had progressed to 124-2 when Rogers was trapped by Anderson for 52, clearly using a pre-arranged plan for the batsman.
Anderson's slower ball was clipped by Rogers to Bell at short midwicket as the bowler and bowling coach David Saker exchanged congratulatory signals between pitch and balcony.
Skipper Clarke and Steve Smith had put on 37 for the fourth wicket when Clarke was induced into the thinnest of edges driving at Broad. Umpire Dar gave it after checking Matt Prior's catch was clean, Clarke reviewed and the sideways hotspot marked up a feather on the bat.
At 161-4 England were once more in the ascendancy and they were scenting blood moments later when Smith was leg before to a Swann ball that turned into his pads and trapped him in front.
Now it was vital for Australia that the two new batsmen - Phil Hughes and Brad Haddin - should survive the best part of an hour to the close.
They survived barely 10 minutes before Swann turned another ball into Hughes' pads. Umpire Dharmasena ruled the delivery had pitched outside leg stump but England boldly reviewed and the ball was just enough in line to earn the reversal.
First innings hero Ashton Agar came to the crease and survived to the close, but the teenager will have to produce something almost as special as his 98 on Thursday if Australia are to win this one.