Pace bowlers Chris Woakes and Liam Plunkett took three wickets apiece.
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They have now won 10 of the last 11 one-day games against Pakistan.
Pakistan are determined to prove the world one-day global rankings wrong as they bid to stay in the Royal London Series.
After a couple of early stumbles in its reply, a third-wicket partnership of 112 between Root and Eoin Morgan (68) put England on course for the win, with Morgan’s knock ending a run of 23 worldwide innings without a half-century.
England lead the five-match ODI series 2-0 and will take on Pakistan with an eye on the series win on Tuesday.
Shoaib Malik (28) went severe on Moeen Ali (0-54) bringing the 50-run stand with Ahmed in the process.
Pakistan had been reduced to 3-2 early in their innings but managed to post something vaguely defendable thanks to a fine backs-to-the-wall century from wicketkeeper Sarfraz Ahmed.
He survived an lbw appeal from the seamer soon after but seven balls later slog swept Rashid straight to Alex Hales on the ropes.
England hardly covered themselves in glory during their run chase at Lord’s, nearly sleepwalking towards victory as they found themselves dragged down to Pakistan’s level. Hales reached 14 without looking entirely comfortable and was bowled by off spinner Imad aiming a big shot on the leg side.
Root provided the reply with a disciplined, doughty spine but fell for 89, his fourth successive half-century in the format, just before the job was done.
After Morgan was bowled by Imad, Ben Stokes scored a typically rapid 42 (from 30 balls) to strengthen England’s position so that even his dismissal and the subsequent loss of Jos Buttler and Root could not prevent an England victory. But the decision of the one-day captain Eoin Morgan will be pivotal, and so far he has not communicated anything other than doubts and reservations.
Unsurprisingly, with a whiff of reverse in the air, Azhar Ali tosses the ball to Wahab Riaz. ‘It makes the fielding innings seem a lot longer when you don’t bowl but I apply myself to my fielding as well.
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The England one-day captain certainly has plenty of options in England’s remarkable rise from one-day laughing stock to the epitome of the modern, powerful limited-overs outfit who should now be targeting a 5-0 series win.
