After losing the toss, Sri Lanka made 377 for eight, Kusal Perera top-scoring with an ODI best 135 and Seekkuge Prasanna making 95 -- his highest score at this level.
Ireland, in reply, were bowled out for 241 with five overs to spare.
Sri Lanka paceman Suranga Lakmal took four for 38 in an innings where Andy McBrine (79) was the only batsman to make more than 36.
Stri Lanka, recently beaten 2-0 in a three-match Test series in England, will now head back 'across the water' for a five-match ODI series against England starting at Nottingham's Trent Bridge ground on Tuesday.