On a rain-truncated day, England managed to come out on top, first by dismissing Australia's six remaining batters for 108 runs to their overnight score of 116-4.
While Stuart Broad and Chris Woakes got three wickets each, Mark Wood and Moeen Ali ended with two apiece.
At Stumps on Day 3, England were 27 for no loss, with 224 more runs needed to win.
This is a must-win match for England if they want to stay alive in the hunt to win back the urn from Australia.
The first two sessions of the day were lost to rain and subsequent delays caused by wet outfield, as the attendees at Headingley patiently waited for the play to resume.
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Once it did, England got down to business, removing Mitchell Marsh and Alex Carey in quick succession, thanks to two stunning deliveries from Woakes.
Travis Head struck a masterful 77, as batters at the other end kept departing. He was dismissed by Stuart Broad to end the Australian innings for 224.
Ben Duckett (18*) and Zak Crawley (9*) will resume Day 4, as England look to bring themselves back into the series after losing their matches in Edgbaston and Lord's.
