The tourists, who scored just 67 in Manchester on Wednesday, were put into bat by England and got off to a fast start, scoring at better than five an over in the early stages before Kusal Perera (19) was acrobatically caught by Chris Jordan off the bowling of Harry Gurney.
That brought Sangakkara to the crease to join Tillakaratne Dilshan (71) and the pair put on a 173-run partnership off 182 balls.
Dilshan's innings came to an end in the 36th over when he failed to make contact with a trademark scoop and had his leg stump removed by James Anderson.
Mahela Jayawardene (7) lasted just 14 balls before he chipped Gurney's delivery to Anderson.
Angelo Mathews was the best of the rest in the final overs as he contributed 30, with Sri Lanka finishing their 50 overs on exactly 300-9.
Gurney was the pick of England's bowlers, finishing with figures of 4-55 off his 10 overs.
Sri Lanka have to win to keep the five-game series alive as they trail 2-1.