Pakistan wicketkeeper Sarfraz Ahmed produced the star turn, making 105 to lift his side to 251 all out, but a lack of support meant that was never likely to be a winning total.
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.
Both Sarfraz and Root favoured pragmatism over pyrotechnics, scoring 61 and 53 singles respectively, but England were collectively stronger and looked in control from first ball to last despite a moderate winning margin and took a 2-0 series lead.
For a side whose 50-over cricket was seen as a basket case little more than a year ago such a drama-free victory is a cause for celebration, but a Pakistan side labelled as “behind the times” by their own head coach, Mickey Arthur, merely logged another reminder of their limitations.
England’s new-ball pairing Chris Woakes and Mark Wood impressed again, sharing six wickets and reducing Pakistan to two for three after they opted to bat first.
Sami Aslam, replacing the out-of-form Mohammad Hafeez, scored one in 10 balls and -departed to the slightest brush of glove off Woakes, third umpire Simon Fry overturning the on-field verdict.
If there was a hint of good fortune about that, the next two overs brought emphatic dismissals.
First Wood uprooted Sharjeel Khan’s off stump with an 87mph beauty that pitched full and seamed perfectly away from the bat, then Woakes unpicked Azhar Ali’s defence with a sharp inswinger.
That brought Sarfraz to the middle and he lingered for the majority of the innings, sharing in successive stands of 64, 59 and 77.
Babar Azam was his first foil, playing fluently for 30 before Liam Plunkett’s brisk yorker dislodged a bail via bat and boot.
Shoaib Malik was in next, adding 28 as Sarfraz steered and guided his way to a calm 50.
Shoaib was comfortable enough against spinners Adil Rashid and Moeen Ali, lifting the latter for the first six of the match, but the returning Wood claimed his edge with a lifter.
Sarfraz continued working steadily towards three figures alongside Imad Wasim and reached the landmark with just his sixth boundary of the day, tucking Plunkett towards fine leg before leaping high in celebration.
Having become the first Pakistani to score a one-day hundred at Lord’s he departed to a half-hit slog-sweep.
That left 7.1 overs, during which England took the last four wickets for 49 runs.
Hasan Ali and Wahab Riaz both fell to memorable catches, Root clinging on at long-leg despite a nasty collision with Rashid and Plunkett collecting a brilliant one-hander.
England would not have been daunted by the chase but the cheap dismissals of Jason Roy, who had his stumps scattered by Mohammad Amir, and Alex Hales, bowled on the sweep by Imad, raised the stakes.
A 10-over score of 39 for two was modest but England were in safe hands – despite Root hobbling after his collision with Rashid.
Hasan was complicit in letting the pair settle, offering Root two cheap fours while Morgan landed a wristy reverse-sweep against Imad.
The pair never looked in jeopardy as they chipped away at the target, Root following in Sarfraz’s footsteps by pushing the ball around with minimal risk and Morgan keener to force the issue.
Pakistan reeled through their bowling options with minimal impact but the stand reached had reached 112 before it could be stopped.
Morgan had been strong against spin but was too ambitious against Imad in the 31st over, shuffling outside leg and letting the ball sneak under an attempted cut.
Root persevered, turning Wahab Riaz for three to bring the target under a hundred, but was happy to play second fiddle to the incoming Ben Stokes.
The Durham all-rounder, still playing as a specialist batsman following calf trouble, was quick to attack.
He peppered the boundary on his way to 42 in 30 balls, also managing an effortless straight six off Yasir Shah, and also received the best delivery of the innings when Hasan dug one into the shoulder of the bat.
Stokes fell in fittingly ambitious fashion, bowled looking for a big hit into the on-side, and Jos Buttler was run out cheaply but the result was safe.
Root was gone before the end, chipping Wahab to Shoaib in search of his century, but Moeen and Woakes applied the finishing touches.
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