Nightwatchman James Anderson was on zero at stumps as the last-ball wicket brought raucous cheers from home supporters on a day of brilliant sunshine at the packed WACA ground.
England's highest successful fourth-innings run chase was the 332 they made to beat Australia in Melbourne in 1928.
If they were to make 391 here, it would be the fifth largest run chase in tests.
"All you can do in these situations is believe," said England fast bowler Chris Tremlett, who took career-best figures of 5-87 in Australia's second innings.
"It's obviously a long shot (to win) but it only takes one partnership and stranger things have happened. We'll come in tomorrow believing that we can win the game."
In Image: A disappointed England's Kevin Pietersen walks off the field