Stokes hit Pat Cummins through the covers for four to complete England's highest run chase in Test cricket, with the Durham all-rounder scoring an unbeaten 135 at Headingley.
Here, the PA news agency looks at five of England's other best Ashes moments on home soil.
Botham's Headingley heroics
Third Test, Headingley, 1981
Leeds has been the scene of an unbelievable England victory before. Australia had a first-innings lead of 227 as England were dismissed for 174 despite Ian Botham's 50. At 135 for seven following on, it looked like England were heading for an innings defeat and going 2-0 down in the series, but Botham's brilliant unbeaten 149 gave the hosts a target of 129 to defend. Botham then took the first Australian wicket before Bob Willis claimed eight for 43 to secure an 18-run victory. England went on to win the series 3-1.
Second Test, Edgbaston, 2005
England had lost eight Ashes series in a row when they hosted Australia in 2005. The tourists had been on course for a 2-0 series lead when an unlikely 10th-wicket partnership between Brett Lee and Michael Kasprowicz took them to within three runs of victory. But with hope slipping away, Steve Harmison got a nick of Kasprowicz's glove, Geraint Jones took the catch and umpire Billy Bowden's finger went up. Commentator Richie Benaud's memorable line has been replayed many times since and the Test has been remembered as arguably the greatest in history – at least until Headingley 2019.
KP brings the urn home
Fifth Test, Oval, 2005
The Edgbaston thriller was followed by two more epic tussles before England headed into the final Test with a 2-1 series lead, needing to avoid defeat to regain the urn. On a dramatic last day, England slipped to 199 for seven as Australia scented a chance of victory. But Pietersen – playing in his first Test series – scored a magnificent 158 to take the game beyond the tourists' reach and win England the Ashes for the first time since 1987.
Jimmy and Monty the unlikely heroes
First Test, Cardiff, 2009
Australia regained the urn with a whitewash Down Under and appeared to be taking an early lead in the first Test of the next series in England when they finally removed Paul Collingwood after his brilliant 245-ball 74. Australia just needed to oust either James Anderson or Monty Panesar to complete an innings victory, but the tail-enders survived for a nerve-jangling 69 deliveries to save the Test. England went on to win the series 2-1.
Fourth Test, Trent Bridge, 2015
Australia headed to Trent Bridge 2-1 down with two Tests to play as they looked to win the series in England for the first time since 2001. They won the toss and elected to bat at Trent Bridge against an England side missing the injured Anderson. But Stuart Broad produced one of the finest spells in Test cricket, taking a staggering eight for 15 as the tourists were skittled for 60 in just 18.3 overs. England went on to win by an innings and 78 runs and reclaimed the urn.