Resuming the final day on 133 for no loss, the opening pair continued their good work until Will Somerville trapped Thirimanne lbw on review after the initial appeal was rejected.
Kusal Mendis (10) looked in a hurry to seal the match as he hit Somerville for a six and a four before his attempted sweep off Ajaz Patel found Jeet Raval at midwicket.
Karunaratne brought up his 100 with his fifth boundary, raising his hands aloft to celebrate the mark.
Kusal Perera made a quick 23 from five boundaries while Angelo Mathews (28 not out) hit the winning run as Sri Lanka romped home in an extended morning session and clinched 60 points in the newly created Test championship.
Captain Dimuth Karunaratne posted his ninth Test hundred as he scored 122