Aggressive pace bowling, with Chris Woakes and Mark Wood taking three wickets apiece, left England chasing a modest target of 252.
Pakistan had collapsed to two for three before Sarfraz Ahmed’s 105, the first ODI hundred by a Pakistan player at Lord’s, and Imad Wasim’s 63 not out kept the tourists in the match. The pair put on 77 for the sixth wicket.
After a couple of early stumbles in their reply, a third-wicket partnership of 112 between Root and England captain Eoin Morgan (68) effectively put the result beyond doubt.
Left-hander Morgan’s knock on his Middlesex home ground ended a run of 23 international innings without a fifty for the former Ireland star.
England’s chase suffered a setback when in-form opener Jason Roy — who made a dashing 65 at Southampton — fell for a second-ball duck as he played on to Mohammad Amir.
Root steadied England nerves with two fours in as many balls off Hasan Ali — a cover-drive followed by a cut. But opener Alex Hales’s lean run continued when he was bowled for 14 trying to slog-sweep left-arm spinner Wasim.
That left England 35 for two but Root and Morgan took the game away from Pakistan, the skipper hitting nine fours before he too was bowled by Wasim.
Ben Stokes made a brisk 42 before Root, whose innings featured just five fours and 53 singles, holed out off Wahab Riaz with England in sight of the winning post at 240 for six.
Woakes ended the match with 15 balls to spare when he cut leg-spinner Yasir Shah, England’s tormentor in chief during Pakistan’s Test win at Lord’s earlier this season, for four.
Pakistan, who saw captain Azhar Ali win the toss and bat on a cloudy morning, lost recalled opener Sami Aslam (one) following an England review after his attempted pull off Woakes was held down the legside by wicket-keeper Jos Buttler.
There was no hot-spot mark but Australian third umpire Simon Fry decide the spike on real time snicko was large enough to give Aslam out.
But there was no doubt at all when Wood dismissed Sharjeel Khan for nought with an express delivery that cut sharply off the seam to knock over the left-hander’s off stump.
Azhar also fell for a duck when caught behind off Woakes. Babar Azam (30) struck several stylish boundaries before he played on to Liam Plunkett.
Pakistan were now 66 for four. But Ahmed, as he’d often done during the preceding 2-2 drawn Test series, frustrated England with a mixture of orthodox and improvised shots.
Shoaib Malik (28) struck a straight six against off-spinner Moeen Ali in a fifth-wicket partnership of 59 before Wood’s return saw him caught behind.
Ahmed, whose lone previous ODI hundred was against Ireland at last year’s World Cup, completed a 124-ball century when he leg-glanced Plunkett for his sixth four.
He then successfully reviewed Plunkett’s lbw appeal before slog-sweeping Ali to Hales in the deep.
Wasim struck Plunkett for three boundaries in as many balls — an uppercut six followed by a straight drive and a cover drive — to go to a 57-ball fifty.
England’s fielding was shoddy at times but Plunkett held a brilliant diving one-handed catch at extra-cover to dismiss Wahab Riaz before No 11 Amir, who took Pakistan to 250 with a boundary, was run out.
The series continues with a day/night match at Nottingham’s Trent Bridge on Tuesday.