Brook, who had already hit three half-centuries in the series, top-scored with an aggressive 85 as England were dismissed for 283 inside 55 overs.
Australia, who lead 2-1 and will claim a first series win in England since 2001 if they avoid defeat, were 61-1, trailing by 222, at the close with opener David Warner the man out.
Having won the toss and asked England to bat in murky conditions, Australia will be content with their day's work and will hope Usman Khawaja (26 not out) can lay the foundations for a first-innings lead on Friday.
Brook had earlier led a counter-attack after England slipped to 73-3, but he fell in the afternoon session as the hosts crucially lost four wickets for 28 runs.
With the Ashes already retained following the rain-marred contest at Old Trafford, Australia are keen to ice the cake with a series win while England have a score to settle after being denied almost certain victory in Manchester.
"They've had a good day bowling us out. When you put a team in, you want to bowl them out in a day. We got up to a respectable total," Brook, who struck 11 fours and two sixes in his 91-ball innings, told Sky Sports.
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Skipper Pat Cummins finally won a toss and not surprisingly put England in. Also unsurprising was the way in which England's openers, Ben Duckett in particular, went about their business.
Duckett struck Mitchell Stark for two boundaries in the fifth over, then flat-batted an 85mph Josh Hazlewood delivery to the ropes in the next, nearly cutting fellow opener Zak Crawley in half at the non-striker's end.
Cummins almost removed Duckett with his first ball of the day but Warner spilled a routine catch at first slip and Crawley was spared as Steve Smith could not cling on to a difficult slip catch off the bowling of Mitchell Marsh.
The missed opportunities were not too costly for Australia as Duckett was out for 41 off 41 balls, gloving a leg-side Marsh delivery behind to Alex Carey.
Crawley (22) went in the next over as Cummins produced a superb delivery that veered in, took an edge, and was pouched by Smith for a record 55th catch in Ashes series.
When Joe Root chopped on to Hazlewood having made only five, England were reeling and Brook was lucky that Carey dropped him off Cummins when he had made five.
A free-wheeling Brook made the most of his reprieve with some rasping strokes, making 48 off 41 balls before lunch, including two fours and a six off one Mitchell Starc over.
Brook and Moeen Ali, who was struggling with a groin injury, continued the assault after the interval with one Cummins over going for 19, including a Moeen six over mid-wicket.
Off-spinner Todd Murphy's second ball was creamed to the boundary by Moeen but then England's wheels came off as they slumped from 183-3 to 212-7.
Moeen was bowled for 34 swiping across the line against the bespectacled Murphy, ending a 111-run fourth-wicket stand. Ben Stokes (3) had his off stump flattened by a beauty from Starc and Jonny Bairstow (4) played on to Hazlewood.
Brook then tried to drive a wide one from Starc but only succeeded in edging to Smith who took a sharp catch.
Chris Woakes was dropped twice as he made 36 in a useful 54-run partnership with Mark Wood (28).
Starc was the pick of the Australian bowlers with 4-82.
In contrast to England's high-octane innings, Australia were measured in reply with Warner and Khawaja rock solid before Woakes struck in the 17th over with Warner fending a delivery to a diving Crawley at second slip.
