Half-centuries from Mathews and Thirimanne - in tough batting conditions - frustrated India on third day in rain-hit opening Test on Saturday.
India will be touring Sri Lanka in March 2018 to play a tri-nation T20 tournament which will also involve Bangladesh.
Pujara stood firm against a persistent Sri Lankan pace attack as the hosts 74-5 at stumps on day two of the rain-hit first Test on Friday.
Bad light and rain halted Sri Lanka process as India struggling with 17-3 on the opening day of the first Test on Thursday.
India had handed Sri Lanka a 3-0 the last time these two teams met in Tests, that too on Sri Lankan soil.
Mendis, Kaushal Silva, Pradeep left out of India tour while fit again Angelo Mathews is back.