Travis Head led the innings with a commanding 170, while Alex Carey contributed 72. The hosts resumed day four at the Adelaide Oval on 271-4, with Head on 142 and Carey unbeaten on 52 after scoring a century in the first innings, News.Az reports, citing foreign media.
The pair added a crucial 162-run partnership before Head was caught in the deep by Zak Crawley. Carey was dismissed shortly afterward, edging to slip.
England then wrapped up the tail quickly, with Josh Tongue emerging as the standout bowler, finishing with figures of 4-70.
England now face a major challenge in the final innings as they chase a large total to secure victory and remain in contention in the Ashes series.
No team has ever chased down more than 316 at the ground, while the biggest successful run chase ever was 418 by the West Indies against Australia at St. Johns in 2003.
Australia lead the five-Test series 2-0 and will retain the Ashes if they win or draw, after back-to-back eight-wicket thumpings in Perth and Brisbane.
