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England had won the toss and put Pakistan in to bat, banking on the pace of fast bowlers Chris Woakes and Jofra Archer for early wickets and no doubt hoping to recreate the way the West Indies skittled Pakistan out for 105 on Friday.
Instead, the visitors put that woeful performance behind them and racked up 348 runs for eight wickets, delighting their cheering fans in the stands with 29 fours and six sixes.
Mohammad Hafeez was his side's top scorer with 84 off 62 balls, while Babar Azam made 63 and captain Sarfaraz Ahmed belted a quickfire 55.
"Everyone was believing we could do this. We were playing good cricket but not winning crucial stages of the game. Everyone chipped in today and gave everything which was required to win the game," Hafeez told the BBC.
"It was a total team effort. It is a very happy dressing room."
Fakhar Zaman and Imam-ul-Haq delighted their vocal supporters by belting a string of boundaries off Archer and Woakes in an opening partnership of 82.
England spinner Moeen Ali finally broke up the pair, getting Fakhar stumped on 36 on his way to a three-wicket haul, while Woakes grabbed three more and also took four catches on a day when England were otherwise uncharacteristically ragged in the field.
Babar and Mohammad Hafeez steadied the ship for Pakistan with a partnership of 88 runs as the visitors set England a larger score than any side had ever chased down in the history of the competition. The best successful World Cup run chase to date came in 2011 when Ireland made 329 against England.
In reply, England steadily lost the wickets of their top-order batsmen Jason Roy, Jonny Bairstow, Eoin Morgan and Ben Stokes to leave the side on 118 for four and give Root and Buttler a mountain to climb.
The two did their best, each eventually reaching three figures. Root hit 10 fours and one six on his way to 107 before scooping an easy catch off Khan to Hafeez at third man.
Buttler smashed a four to notch up his own hundred a few overs later, only to fall to the very next ball.
As the balls-remaining count dwindled, Moeen and Woakes swung valiantly at everything they could. But after they were both caught out in successive balls, Mark Wood and Adil Rashid were left stranded at the crease as the target slipped beyond their reach.