Pakistan recovered from a dreadful start, thanks to a century by Sarfraz Ahmed, to post a respectable total of 251 before Root and captain Eoin Morgan shared a third-wicket stand of 112 to lay the platform for the hosts to go 2-0 up in the series.
England opener Jason Roy fell to the second ball of the innings, bowled by Mohammad Amir, but Root looked in complete control from the start while Morgan made a busy 68 including nine fours.
Ben Stokes chipped in with 42 and although England lost wickets at regular intervals, they reached their target with more than two overs to spare.
Pakistan slumped to two for three after winning the toss, Chris Woakes taking two wickets and Mark Wood one in a fiery opening burst by the England pace attack.
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Babar Azam and Sarfraz steadied the innings with a fourth-wicket alliance of 64 before Azam was bowled by Liam Plunkett for 30.
Sarfraz played sensibly in the circumstances and found another reliable partner in Imad Wasim as the wicket-keeper hit six fours on the way to a second one-day international century before he was out for 105.
Wasim finished unbeaten on 63. Wood and Woakes took three wickets each.
The third game in the five-match series is in Nottingham on Tuesday.
(Reporting by Ed Osmond; Editing by Tony Jimenez)
