Australia ended the third day at 169-6 after Bresnan claimed the crucial wickets of Shane Watson, Ricky Ponting and Michael Hussey shortly after tea. The home side still trails by 246, after England was out for 513 at lunch.
England dismissed Australia for a paltry 98 on the first day.
Bresnan, who replaced Steven Finn in England's bowling attack for the fourth Test, ended the day with figures of 3-26 off 15 overs with 7 maidens.
“I think I do like the big occasion and I do like to be under pressure. I think it brings out the best in me,” Bresnan said.” So why wouldn't it be on Boxing Day in Australia.” Brad Haddin will resume the fourth day on 11 with Mitchell Johnson on 6. With just four wickets remaining and two days still to play, a loss appears inescapable.
“It's very shattering to be in the position we are now,” Watson said. “After playing so well in Perth and feeling like we're a big chance of being in the series and winning the Ashes to be in the position we are after our poor performance.” With a win, England will take a 2-1 lead into the final match starting Sunday at Sydney, but as Ashes-holder needs only to draw the series to retain the urn. England hasn't won an Ashes series on Australian soil since the 1986/1987.
Bresnan said the England players were upbeat ahead of the fourth day, but were holding off their celebrations.
“We've had a good day, but we realize we've still got four wickets to get,” he said.
The Australian openers made a bright start to the second innings and scored confidently in a 53-run partnership until Phillip Hughes was run out in the 12th over after Watson hesitated between the wickets while looking for a single.
Watson was trapped lbw for 54 straight after tea when tempted by a swinging Bresnan delivery.
Australia captain Ponting, who made just 10 runs in Australia's disastrous first innings, was unable to make amends and managed 20 in the second before being bowled by Bresnan.
Hussey failed to reprise his usual role as anchor of the Australian middle order, departing for a duck after skying a catch to Ian Bell at short extra-cover.
“The way he bowled today was brilliant,” Watson said of Bresnan. “It's what I expected him to do because he's a high-quality bowler.” Michael Clarke also failed to contribute, making 13 runs before being caught by Andrew Strauss at second slip off a Graeme Swann delivery. Steven Smith was bowled by James Anderson for 38 shortly before stumps.
Earlier, seam bowler Peter Siddle (6-75) continued to carry the Australian attack, claiming Anderson (1) as his sixth wicket with the final ball before lunch as England ended its first innings with a massive 415-run lead.
Jonathan Trott still dominated the Australian bowlers, ending the innings on an unbeaten 168 after resuming the day on 141. He appeared untroubled by a knock to his knee from an inside edge Monday, and played his shots with ease.
Siddle had Matt Prior caught for 85 by Ponting at mid-on to end a 173-run partnership with Trott for the sixth wicket. Siddle took his fifth-wicket four overs later when he had Bresnan caught behind for 4.
Ben Hilfenhaus (2-83) took just his third wicket of the series when Swann was caught behind on 22. He then bowled Chris Tremlett for 4.
Australia's bowling stocks took a major blow when paceman Ryan Harris broke down with a stress fracture to his left ankle while running in to Bresnan. Harris sank to the ground before limping from the field with Australia medical staff. It is unknown if he will bat this innings.
