Brook’s innings took him to fifth on England’s all-time list while his monster stand with Root easily eclipsed the previous best of 411 between Peter May and Colin Cowdrey, against the West Indies in 1957.
Only three pairings globally have ever put on more than the Yorkshire duo and they leapfrogged even Sir Donald Bradman’s highest partnership (451 with Bill Ponsford versus England at The Oval in 1934) by three runs before giving way.
England, who conceded 556 in the first innings, somehow flipped that into a lead of 267, but it became even better as Pakistani wickets began to tumble.
England’s merciless scoring appeared to break the home side’s spirit - the dejected looking bowlers, lethargic ground fielding, the truly terrible catching - but Pakistan’s top-order implosion confirmed they had lost heart for the fight.
They lost opener Abdullah Shafique to the very first ball of their second innings, thanks to fine skill from Chris Woakes, nipping in and sending off stump spiralling.
First-innings centurion Shan Masood then survived two drops before chipping Gus Atkinson to short midwicket for 11 and the Surrey seamer had Babar Azam caught behind moments later.
Debutant Brydon Carse then took out Saim Ayub with his loosener, well caught by the retreating Ben Duckett at mid-off, and bowled off-form Mohammad Rizwan.
After just 13 wickets had fallen in the first 10 sessions of the match, Pakistan conspired to lose five in 12.1 overs. Jack Leach made it six when he had Saud Shakeel caught behind but a four-day win slipped through Shoaib Bashir’s fingers as he dropped Aamer Jamal at fine-leg to deny the impressive Carse.
Earlier, Yorkshiremen Root and Brook put on 166 in 29 overs. Root was badly dropped at midwicket on 186 by Babar, and Jamie Smith was later put down twice in a late cameo as heads dropped.
Root reached 200 for the sixth time in his career and accelerated past 250 with a reverse scoop. Brook ticked off his Test best of 186, his first-class best of 194 and made his double-ton in 245 balls.
He brought up the 400-run partnership with a cheeky uppercut for four and, after being interrupted by lunch, ended May and Cowdrey’s 67-year record in the first over of the afternoon.
Root finally gave way after 10 hours at the crease when he was lbw to Agha Salman but Brook went on to become just the sixth Englishman to reach 300.
A top-edged sweep brought him up short of Len Hutton’s record of 364 and, like Root, he was mobbed with handshakes by the opposition as a mark of respect on his way to the pavilion.
