Harry Tector provided some resistance for Ireland but Sri Lanka bowled them out 10 runs short of their first-innings lead.
Sri Lanka declared on a mammoth 704-3 in their first innings.
Dimuth Karunaratne and Nishan Madushka put on an opening partnership of 228 as Sri Lanka were dominant on day three of the second Test against Ireland
Ireland take charge in Sri Lanka with highest Test score of 492.
Balbirnie, Stirling and Tucker scored half-centuries after the visitors had been reduced to 89 for 3 in the first session in Galle.
Jayasuriya picks up ten in the Test as Sri Lanka roll Ireland over for innings victory.
The tourists laboured to 117-7 in reply to their hosts' first innings total of 591-6 declared.
Sri Lanka have announced their 15-member squad for the first Test against Ireland which will begin on April 16 in Galle.
Sri Lanka tour format changed to two Tests as ODIs are dropped.
