Sri Lanka, in their second innings, were 86 for four, a deficit of 68 runs.
Michael Vandort was 30 not out and Tillakaratne Dilshan 21 not out. England totalled 295 on Friday in reply to Sri Lanka's first innings 141.
Kevin Pietersen scored 142 and Sri Lanka off-spinner Muttiah Muralitharan took six for 86.
The three-match series was level at 0-0 after the first Test was drawn.