England need another 224 runs to win the third Test and keep their Ashes hopes alive after a thrilling rain-shortened third day at Headingley.
The hosts survived a tricky spell to reach 27-0 at the close, chasing 251.
Australia slipped from 116-4 to 170-8 in perfect bowling conditions after rain prevented play until 17:00 BST.
Travis Head batted superbly to help add another 54 for the final two wickets before he fell for 77 as the tourists were dismissed for 224.
Defeat for England will see Australia win an Ashes series in England for the first time since 2001.