Sri Lanka declared their first innings on a mammoth 591-6 before reducing Ireland to 117-7, still needing another 274 to avoid the follow-on.
Lorcan Tucker was batting on 21 at the close, with Andy McBrine alongside him on five.
Playing only their fifth-ever Test, and seeking their first win since attaining the status in 2017, Ireland could only demonstrate their weakness against a team ranked seventh in the world in the five-day format.
Left-arm seamer Vishwa Fernando – playing his first Test in 10 months – dismissed Murray Commins for a golden duck and captain Andy Balbirnie in just the second over of the Ireland innings. Harry Tector (34) and James McCollum (35) put together a 70-run partnership before left-arm orthodox spinner Jayasuriya wreaked havoc with a double wicket maiden, claiming the scalps of Tector and Curtis Campher.
SCOREBOARD
Sri Lanka first innings (overnight 386-4)Nishan Madushka c Tucker b Campher 29
Dimuth Karunaratne c Tucker b Adair 179
Kusal Mendis lbw b Dockrell 140
Angelo Mathews c Tucker b White 0
Dinesh Chandimal not out 102
Prabath Jayasuriya lbw b Campher 16
Dhananjaya de Silva lbw b McBrine 12
Sadeera Samarawickrama not out 104
Extras: (b4, lb3, w1, nb1) 9
Total: (for 6 wickets, overs 131) 591/d
Fall of wickets: 1-64 (Madushka), 2-345 (Mendis), 3-348 (Mathews), 4-373 (Karunaratne), 5-390 (Jayasuriya), 6-408 (de Silva)
Bowling: Mark Adair 24.3-3-95-1 (w1), Curtis Campher 21-2-84-2, Andy McBrine 40-2-162-1, Benjamin White 22-0-119-1 (nb1), George Dockrell 21.3-0-112-1, Harry Tector 2-0-12-0
Ireland first innings
James McCollum b Jayasuriya 35
Murray Commins b V. Fernando 0
Andy Balbirnie c Madushka b V. Fernando 4
Harry Tector c de Silva b Jayasuriya 34
Curtis Campher c Mendis b Jayasuriya 0
P Moor c Samarawickrama b Jayasuriya 14
Lorcan Tucker not out 21
George Dockrell lbw b Jayasuriya 2
Andy McBrine not out 5
Extras: (nb2) 2
Total: (wickets 7, overs 45) 117
Fall of wickets: 1-0 (Cummins), 2-4 (Balbirnie), 3-74 (Tector), 4-74 (Campher), 5-85 (McCollum), 6-92 (Moor) 7-108 (Dockrell)
Bowling: Asitha Fernando 5-2-9-0, Vishwa Fernando 6-1-22-2, Prabath Jayasuriya 19-9-42-5, Ramesh Mendis 14-3-40-0 (nb 2), Dhananjaya de Silva 1-0-4-0