Trailing 2-0 after defeats in Brisbane and Adelaide, England need at least a draw at the WACA to ensure the five-match series is still alive when it moves to Melbourne.
England paceman James Anderson broke Steve Smith and Mitchell Marsh's 301-run stand with the second ball of the morning but Australia still pushed to 643 for seven, and a first-innings lead of 240, by lunch on day four of the third Ashes Test.
Trailing 2-0 after defeats in Brisbane and Adelaide, England need at least a draw at the WACA to ensure the five-match series is still alive when it moves to Melbourne. Their hopes of saving the Test may rely on the weather, however, with showers forecast later on Sunday and on day five.
Australia resumed on 549 for four, with captain Smith on 229 and Marsh on 181, but all-rounder Marsh fell lbw to Anderson and was unable to add to his overnight total on a sunny, breezy morning at the WACA. The wicket triggered a mini-collapse as Australia lost 3-12, with Smith and Mitchell Starc quickly following Marsh back to the dressing room.
But wicketkeeper Tim Paine and Pat Cummins steadied the home side with an unbeaten 82-run stand. Paine was 41 not out and tailender Cummins 36. Australia's total is the second highest recorded at the WACA, behind only the home side's first-innings 735 for six declared against Zimbabwe in 2003.
Anderson trapped Smith lbw for 239 and Starc ran himself out for one with a poor call for a single after a deflection off Paine's pads went straight to the man at gully. England's hopes of rattling through the tail were dashed, however, as Paine and Cummins played watchfully and grew in confidence against the new ball.
Alarmingly for the tourists, the pitch is showing increasing variable bounce with a big crack opening up in front of the crease at the southern end. One Stuart Broad delivery hit the crack and was unplayable, fizzing away from Paine's bat like a legbreak. Cummins hit out in the final over before lunch, clubbing Moeen Ali for a four and slog-sweeping him for a big six in consecutive balls.
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