England 237 (Stokes 80, Cummins 6-91) and 254 for 7 (Brook 75, Starc 5-78) to beat Australia 263 (Marsh 118, Wood 5-34) and 224 (Head 77, Khawaja 43, Broad 3-45, Woakes 3-68) by seven wickets
Leeds: England kept their Ashes hopes alive by beating Australia by three wickets in another nerve-shredding Headingley finale.
Harry Brook hit a superb 75 but it was left to bowlers Chris Woakes and Mark Wood to drag the hosts over the line in pursuit of 251.
Brook's mature knock took them to within 21 of victory, after talisman Ben Stokes fell for 13 following lunch with 90 still needed.
Brook put on 59 with Woakes before top-edging a cut off Mitchell Starc, who almost won the series for Australia with a vicious 5-78.
That wicket brought Wood to the crease amid gripping tension and he hit Pat Cummins for six and thrashed Starc for four to spark jubilant sin the stands.
With four needed, Wood was dropped by Australia wicketkeeper Alex Carey and Woakes, who finished unbeaten on 32, slashed the winning runs.
England's makes the series 2-1 to Australia with two Tests to play, setting up a grandstand finale that could yet match the iconic contest in 2005.
There is a nine-day break before the fourth Test at Old Trafford starts on Wednesday, 19 July.
Earlier, Starc's quick strikes in the day failed to trigger the collapse that Australia would have hoped for in the first session on day four. Ben Duckett, who was a thorn in Australia's side in the previous Test match, was trapped in front by Starc in the 10th over of the innings.
England sent Moeen Ali in at No.3 in a surprising move with Harry Brook, who played at the spot in the first innings, moving down below Joe Root to No.5.
The ploy didn't work for Moeen, though, as he was cleaned up by Starc for just five runs.
Joe Root joined a positive Zak Crawley and together the duo rebuilt for England. The partnership got off to a quick start, but just as Australia were being pushed out of the game, Mitchell Marsh struck with his medium pace.
The seamer found the edge of Crawley's bat and England had lost a third wicket before reaching three figures.