For a time Sri Lanka threatened the target, with opener Dimuth Karunaratne striking a run-a-ball 120. The hosts needed 84 off the last 10 overs with seven wickets in hand, however they lost four for two, including three in one over from lively Adam Milne to end their pursuit.
Spinner Anton Devcich continued a good tour with three for 58, Milne took three for 57 and Andrew Ellis two for 43.
The second game is on Tuesday night in Dambulla.
Scores: New Zealand A 350-8 (L. Ronchi 84, C. Munro 70, A. Kitchen 62, A. Ellis 46, S. Kuggeleijn 43 not out; S. Serasinghe 2-46, D. Perera 2-46) bt Sri Lanka A 322 (D. Karunaratne 120, D. Chandimal 69, A. Priyanjan 27; A. Milne 3-57, A. Devcich 3-58, Ellis 2-43) by 28 runs.