England 237 (Stokes 80, Cummins 6-91) and 27 for 0 need 224 more runs to beat Australia 263 (Marsh 118, Wood 5-34) and 224 (Head 77, Khawaja 43, Broad 3-45, Woakes 3-68)
Leeds: 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 reached 27-0 at the close, chasing 251, after bowling Australia out for 224.
England took advantage of perfect bowling conditions to turn Australia's 116-4 into 170-8 after rain prevented any play until just before 17:00 BST.
At that stage Australia's lead was 196 but Travis Head batted superbly to help add another 54 for the final two wickets.
He batted in the style of Ben Stokes, striking seven fours and three sixes, in his 77 before being caught in the deep.
That left England with a perilous 25 minutes to bat but Zak Crawley and Ben Duckett hit four fours in five overs to give England a platform.
Defeat for England will see Australia win an Ashes series in England for the first time since 2001.
England's bowlers - first through Chris Woakes and backed up by Mark Wood and Stuart Broad - grabbed the momentum, only to see it snatched away by Head's belligerence as darkness turned into bright evening sunshine.
Crawley began England's chase by clipping to the mid-wicket fence in the first over. In the next English hearts raced as Duckett survived a review for a catch down the leg side and edged short of second slip off Mitchell Starc.
An over later Duckett was hit on the glove by Pat Cummins. He responded by thrashing the Australia captain through the covers before driving him down the ground for four.
England's openers left the field to a rapturous reception, the hosts with their noses in front by a slither.
After the long wait, Woakes gave England an ideal start by removing Mitchell Marsh in the third over of the day.
The first-innings centurion biffed two fours in the gloom but only added 11 to his overnight score before he gloved Woakes behind when trying to leave.
Woakes saw off wicketkeeper Alex Carey for five in similar fashion, this time the ball deflected onto stumps as the left-hander withdrew his bat.
That exposed the tail and England turned to fast bowler Wood.
First Wood removed Starc, who chipped a bouncer in the air for Harry Brook to run and take a smart catch, while Cummins added just one before he offered a thin edge behind.
That brought in Ashes debutant Todd Murphy but he impressively hit Wood for four first ball.
Despite the gloom, England continued their short-ball theory to Head and he attacked it with increasing intent - hitting Wood over the leg-side rope in successive balls.
England were struggling as he attacked but Broad, who also trapped Murphy lbw for 11, had him caught at deep mid-wicket to end the innings.