India restricted the hosts to 212 under lights after posting 258 for an unbeatable 3-1 lead in the five-match series.
It was their first-ever bilateral one-day series victory in Sri Lanka.
The tourists were well-served by batsmen Suresh Raina (76), skipper Mahendra Singh Dhoni (71) and teenager Virat Kohli (54) before off-spinner Harbhajan Singh bagged three wickets, including that of Jayasuriya.
Left-handed opener Jayasuriya posed the main threat to India, giving a magnificent display of power-hitting to smash two sixes and eight fours in his 52-ball 60.
"We are a good fielding side and that is a plus point. Raina played well, but it was disappointing that we both got out together and could not get runs in the end," Dhoni said.
Indian seamer Munaf Patel removed Malinda Warnapura for no score and out-of-form Kumar Sangakkara (six) in three overs t