Root helped England to 324-7, sharing a 109-run stand with Jos Buttler, who made 70 off 45 balls.
David Willey took 4-34 and Liam Plunkett 3-44 to help Sri Lanka out for 202 with 7.2 overs unused.
Sri Lanka are still without a win against England on this tour, with only Tuesday’s Twenty20 remaining.
England move above Sri Lanka to fifth in the International Cricket Council rankings, and look a different side to the one that exited last year’s World Cup at the group stages.
James Vince, who struggled in the Test series against the same opposition, did well to make a maiden ODI half-century but threw his wicket away when trying to cut loose off the spin of Danushka Gunathilaka, who took 3-48.
In the run chase, Gunathilaka’s 48 proved useful after some early wickets, but after his dismissal to Plunkett only Dinesh Chandimal could provide some resistance with 53 until he was bowled by Willey.
On a pitch that had looked to favour seam bowling, spinner Adil Rashid picked up 2-41 in 10 overs, and Willey returned late on with two 41st-over wickets before sealing victory in his next.
Man of the match Buttler’s reputation for lower-order hitting served him well, in the cause of boosting England’s run rate.
The hosts were on 227-4 after 40 overs, and with Root, who faced 106 balls, playing a relatively pedestrian innings, Buttler provided the impetus with a strike rate of 156.
The Lancashire man pulled out the novelty shots, taking four fours off Nuwan Pradeep, and also ran well between the wickets during his 14.2-over alliance with Root.
The hosts have had a very productive one-day series, despite the stumbles in the tied opener at Trent Bridge.
Leading scorer Jason Roy scored 316 runs, including two centuries – he was named man of the series – while Plunkett, Willey and Adil Rashid excelled well with the ball.
England can now look ahead to the visit of Pakistan – the Test series starts on 3 July and the ODI series on 18 August – with confidence. (Courtesy BBC Sport)