Ravi Bopara top-scored with 51 and Joe Root made 42 in a game reduced to 45-overs-a-side after the start was delayed by wet weather.
Ajantha Mendis claimed three for 33 and Tillakaratne Dilshan and Dhammika Prasad took two wickets each.
Sri Lanka lead 1-0 in the seven-match series, having won the first game by 25 runs on Wednesday.