Asela Gunaratne was Sri Lankas top scorer with 36 off 37 balls.
Dasun Shanaka played a handy knock down the order with 29 off 24 balls including two sixes.
Dushmantha Chameera took two for 22 as Sri Lanka managed to restrict India at the start of the chase.
Hardik Pandya took two wickets to clean up the lower order.
Jaydev Unadkat once again was successful in dismissing Niroshan Dickwella.
Rohit Sharma (27) and Shreyas Iyer (30) were crucial in building a partnership of 22 runs.
Shanaka also picked up two for 27 in four overs.
MS Dhoni and Dinesh Karthik put on a 31-run partnership to seal a 3-0 series win for India.
Pandey scored 32 off 29 balls and was India's top scorer.jpg
Shreyas and Manish Pandey put on a 42-run partnership for the third wicket.