Three Sri Lanka batsmen -- Dinesh Chandimal (62), captain Angelo Mathews (56) and Kusal Mendis (53) all made fifties.
Chris Woakes took three for 34, including two wickets with his last two balls, after fellow paceman Liam Plunkett made early inroads on his way to a return of three for 46.
England lead the five-match series 1-0 after their 10-wicket win at Edgbaston on Friday. That followed Tuesday's tie at Trent Bridge.