On a beautifully sunny day at The Oval, England set Australia 399 to win and bowled them out for 263 to square the contest with their oldest enemies in a year when they lifted the World Cup for the first time.
Australia retain the urn they won in 2017-18 but miss out on a first series win in England since 2001, while an Ashes series is drawn for the first time in 47 years.
From 313-8 overnight, England added 16 to be all out for 329 and leave Australia in need of pulling off the highest run-chase in an Ashes Test since 1948.
In conditions that remained relatively good for batting, there was the slightest chance that Steve Smith could end his prolific summer with one more stroke of genius.
There was disbelief, then delight, when Smith turned Stuart Broad to a diving Ben Stokes at leg slip for 23 - his lowest score of the series by 57 runs.
England were still held up by Mathew Wade's combative century, but after he was stumped off Joe Root, the last three wickets fell for four runs, with victory completed by Root's stunning grab of Josh Hazlewood.
It means they end coach Trevor Bayliss' reign with a win, while both sides have 56 points and sit joint-fourth in the World Test Championship.
Even though the Ashes were already gone, captain Root challenged England to begin their preparations for the tour down under in 2021-22 in this match.
They were helped by Australia's decision to field first, strange team selection and dropped catches, but also earned this win through the batting of Joe Denly and Jos Buttler, and a collectively incisive bowling attack.
If Broad removing David Warner for the seventh time in the series was expected, the scale of the celebration inside The Oval was only surpassed when Smith fell.
There was the theatre of Jofra Archer's duel with Wade, complete with crossed words and long stares, and one more magical moment when Root took his wonderful grab as the shadows lengthened.
No doubt it was the dream for England to lift both the World Cup and the Ashes, but being crowned world champions for the first time and drawing with Australia will be regarded as a success.
Still, Bayliss' successor has immediate work to do - finally nailing down a top order, getting the best from Root as batsman and captain, deciding the best make-up of the attack - starting with the tour to New Zealand in November.