Leach leads England's record-breaking rout of Pakistan in first Test
England's attack made short work of the last four Pakistan batters on day five, dismissing the hosts for 220 to win by an innings and 47 runs and draw first blood in the three-match series.
The win is England's fourth consecutive Test triumph on Pakistan soil, after a 3-0 whitewash two years ago. England had only won two away Tests against Pakistan in the previous 61 years.
It was also filled with several new milestones for England.
"This win would be right up there. Definitely top three," said captain Ollie Pope, standing in for injured skipper Ben Stokes.
Brook smashed 317 and Root a record-setting 262 in England's mammoth 823-7 declared, giving the visitors a 267-run lead and both players their highest Test scores.
Their 454, England's highest-ever partnership for any wicket in Test cricket, also delivered an improbable advantage after Pakistan amassed an impressive 556 first-innings total.
Pope was full of praise for Brook and Root's heroics.
"Credit to them for the skills and determination to put the team in a winning position," he said.
By close of play on the fourth day on a lifeless pitch, England had posted the fourth-highest Test innings total of 823-7 and taken total control of the match with the hosts teetering at 152-6.
Along the way, Root became the highest run scorer for England in Test history.
England's bowlers then delivered a dagger blow on a lifeless Multan pitch where the first 17 wickets fell for a mammoth 1,379 runs.
Towards the end of the fourth day, Pakistan were reeling at 82-6 before Salman Agha and Aamer Jamal came together for Pakistan's only meaningful partnership.
The pair added 109 before Leach, who marshalled the attack with 4-30, provided the first breakthrough on the fifth day when he dislodged Salman for a fighting 63 and opened the floodgates.
Leach then took a smart return catch to get Shaheen Shah Afridi for ten and then had Naseem Shah stumped for six, wrapping up Pakistan's second innings.
Last man Abrar Ahmed was unable to bat after being taken to hospital with a high fever.
"When you come out to bat again and you're 260 runs behind and the pitch is three days older, it's never easy," said Pope of Pakistan's second-innings predicament.
Pope also lauded the grit shown by England's inexperienced attack.
"Our bowlers got the odd ball to reverse and spin," he said of Gus Atkinson who took 2-46 and debutant Brydon Carse who finished with 2-66.
'Can't be more disappointing'
The loss continues a painful losing stretch for Pakistan and will compound the pressure on captain Shan Masood.
His tenure has begun with six consecutive defeats, including three in Australia and two at home at the hands of Bangladesh.
"It can't be more disappointing than this," said Masood. "Harsh reality is that England found a way to win after two days under the sun and 556 behind.
"Then they batted big and when they came back with the ball they had a plan and created a window of opportunity in the second innings so the harsh reality in Test cricket is no matter what the pitch quality side finds a way to win."
Pakistan's collapse marked a quick turnaround to the match after a flat Multan stadium pitch saw 1,379 runs scored for the loss of just 17 wickets.
The hosts have gone 11 Tests without a win on home grounds, their last win against South Africa came in February 2021.
The second Test starts at the same venue from Tuesday while the third is in Rawalpindi from October 24th.