Had Eng managed a few more runs, the series could well have been tied 2-2 after four games.
Sangakkara and Jayawardene put on 96 for the third wicket.
Sangakkara went for a square drive off a short ball from Jordan but ended up finding Woakes at point.
Mahela Jayawardene was cleaned up by Chris Jordan.
Sangakkara and Jayawardene put on yet another 50-run stand.
Perera could only manage 31 before giving Chris Jordan a catch at slip off Moeen.
Dilshan was batting well before he tried to heave one over covers.
Eoin Morgan's 65 came off just 47 balls.
Bopara was bowled by Tillakaratne Dilshan.
James Taylor's 90 was his career-best effort.