Root anchored the innings after England’s shaky start in pursuit of a modest 205-run target, reaching his half-century off 108 deliveries.
The hosts lost opener Ben Duckett for 11, caught behind by Kusal Mendis, and captain Ollie Pope followed soon after, caught at slip for six.Milan Rathnayake then trapped Dan Lawrence lbw for 34. Harry Brook contributed 32 in a 49-run partnership with Root before falling to Prabath Jayasuriya, leaving England in a precarious position at 119-4.
Smith, who scored his maiden Test century in the first innings, displayed patience alongside Root as England went an hour without finding the boundary. The hosts regained control before Asitha Fernando bowled Smith for 39. Root, unbeaten on 62, hit only his second four off the final ball to seal England’s 1-0 lead in the three-match series.
Earlier, Sri Lanka resumed the day at 204-6, with Kamindu Mendis and Dinesh Chandimal batting through the rain-affected first session, adding 117 runs for the seventh wicket and pushing the visitors past 300.
Kamindu scored his third Test century, showcasing sublime shot-making and tireless running between the wickets. He has quickly become one of Sri Lanka’s most consistent Test players, with three centuries and two half-centuries in his eight innings.
However, Kamindu fell to Gus Atkinson shortly after lunch, nicking one to Root as England capitalized on the new ball, despite fast bowler Mark Wood being sidelined for the day with a thigh injury.
Matthew Potts dismissed Chandimal for 79, who battled through pain after injuring his thumb, as Sri Lanka’s innings concluded on 326, adding just 19 runs for the last three wickets.
The second Test is set to commence at Lord’s on Thursday.