Ben Stokes has 'no hesitation' England can complete Ashes comeback after third test win
Chasing 251 to win at Headingley, England slumped to 171-6.
Harry Brook's 75 put the hosts back in command before Chris Woakes (32 not out) and Mark Wood (16 not out) got Stokes' men over the line.
Australia still lead the best-of-five series 2-1 and need just one more win to secure their first Ashes triumph in England for 22 years.
But Stokes remains confident England can become just the second team to win a Test series from 2-0 down after the Don Bradman-inspired 1936/37 Australia side that won the Ashes.
"Yep. No hesitation," said Stokes when asked if England can win the series.
"Another down-to-the-wire game. It's nice to get over the line in this one and keep our hopes alive."
Stokes' 155 was not enough as England fell just short in a run chase in the controversial second Test at Lord's last week.
But he and the selectors could afford themselves a pat on the back as the three changes they made to the side paid dividends.
Woakes and Wood starred with both bat and ball, while Moeen Ali took the key wickets of Marnus Labuschagne and Steve Smith in Australia's second innings.
"It's great when you make decisions like that and they have a big impact on the team," added Stokes.
"We want people to come in and impact the game in their moment to put us in a commanding position and all three guys did that."
Wood won player of the match in his first Test since December last year after taking 5-34 in Australia's first innings and a first-innings cameo of 24 runs off eight balls with the bat.
"I am delighted to be stood here and great for us to win the match and it keeps the series alive," said Wood.
"It is the first time I've got England over the line with the bat so I'm delighted."
Australia captain Pat Cummins was left to rue a few key moments in the match that got away from his side after they won two tight Tests to take a commanding lead in the series.
The tourists collapsed from 240-4 to 263 all out in their first innings and allowed England to recover from 167-8 to narrow the gap at the halfway stage of the game to just 26 runs.
"It seems like a series where one session swings in one team's favour and then the next session the other team picks it up," said Cummins.
"Unfortunately it happens. I thought getting up to 250 gave us something pretty competitive to bowl at but it wasn't quite enough."
The fourth Test of the series gets underway at Old Trafford in Manchester on July 19th.