England put itself in pole position for an Ashes-leveling win after leaving Australia a record chase after another display of “Bazball” bravado which has had mixed results during the series but has always entertained.
The hosts turned in a swaggering attacking performance in south London as they ushered an enthralling series towards its end game.
Root was undone by a shooter, Crawley signed off a fine summer and Bairstow enjoyed clubbing bowlers as the tourists chased leather for 80 overs.
It was a fitting way for England’s batting unit to bow out after six weeks of fearless - and often reckless - hitting with 48 boundaries and three sixes.
Broad, England’s second-highest test wicket-taker of all time after Anderson, announced he would be retiring from all cricket at the end of this match.
There are two days left, with weather unlikely to play a significant role - as it did in the fourth test - on a ground where the highest fourth-innings pursuit sits at 263, while Donald Bradman’s “Invincibles” are the only Australian team to have chased more.
Australia established a slender lead of 12 before being bowled out in the final act of the second day, an advantage that lasted precisely an over on Saturday.
The first ball of the day was a wide half-volley from Starc, practically begging to be crashed through the covers for four. Crawley had done exactly that to the opening ball of the series back at Edgbaston and needed no encouragement to repeat the stroke.
A single and two boundaries from Duckett followed in quick succession, clearing the deficit in six balls. For an Australia side which had scraped just 13 runs off the bat in the first hour on the second day, England’s self-assured start seemed disorientating.
Starc was hauled off after shipping 22 from two overs - a poor spell even by T20 standards, let alone an Ashes test - with Australia unable to plug the scoring. England reached 50 in 8.4 overs, with Duckett collecting seven fours.
The touring attack was light on ideas but finally made a breakthrough with 79 on the board, when the returning Starc had Duckett caught behind off a thin edge. England was not allowed to send out Moeen Ali due to time spent off the field with a groin injury, leaving Stokes to become his side’s fourth No 3 of the series.
England romped along to 130 for one at lunch.
Crawley was in sight of reaching 500 runs for the series, a landmark few would have tipped him to get close to at the start, but fell 20 short when he drove slightly lazily at Pat Cummins’ delivery that shaped away.
That was the first of three wickets in the afternoon session. Stokes made 42 before hacking Murphy to mid-on and Harry Brook (7) hit one huge straight six before nicking Josh Hazlewood behind, but this was Root’s time to take the spotlight.
After surviving a marginal lbw shout on four, he came to life. Mitch Marsh was reverse ramped for six over third man, a party trick that never loses its sparkle, and flicked fine to fine-leg when he straightened up in response.
Starc, meanwhile, conceded three consecutive boundaries culminating in a loose-limbed uppercut. Root’s half-century took just 42 deliveries and by the time tea arrived, he and Bairstow had already pushed the lead past 250.
Bairstow seemed particularly hungry to hurry along, depositing Murphy through the covers and popping him back over his head, then tucking into his favorite cut shot to give Hazlewood a dose.
By the time his frenzy took the fifth-wicket stand to 100, he had scored 70 of them. Root was quietly making his way toward his own century, until he was cut off by a grubber from Murphy.
The bowler can take credit for generating some handy turn, but Root had no chance as the ball skidded into his stumps off the toe end. Bairstow followed with a flat-footed poke at Starc and the innings wound to an end in a flurry of activity.
The ailing Moeen made 29 in what is surely his final test innings, but joined Chris Woakes and Mark Wood in donating his wicket chasing quick runs at the close.