Recalled after a gap of more than one year, the left- handed Thirimanne was dropped by Shikhar Dhawan off Umesh Yadav in the slip cordon when he was on 27.
The Sri Lankan vice-captain made full use of dropped chance to frustrate India along with Mathews (batting 31), stitching an unbroken patnership after Bhuvneshwar Kumar (2/38) evicted both the openers.
Sri Lanka also put up a spirited bowling effort in the morning session by dismissing India for 172, their second lowest score against Sri Lanka at home.
Everything fell in place for the tourists as not only did they called two fine reviews to changed the course of the game but luck too aided them.
Having taken a fine review to overturn umpire Joel Wilson's decision and dismiss Ravindra Jadeja Sri Lanka took another review successfully this time while batting for opener Dimuth Karunaratne.
The left-handed opener was given out trapped in front by Mohammed Shami but they reviewed successfully as the opening duo took Sri Lanka to 29 after four overs.
It was not the case to be as Thrimanne and former captain Mathews, who is promoted to four in his comeback match, put on a composed approach in their left-right combination.
Barring the blip Thirmianne was dropped by Dhawan, the Lankans did not take a step wrong as it turned out to be another frustrating session for the home team.
Earlier, coming out to bat at an overnight score of 47, Cheteshwar Pujara (52 off 117, 10x4) completed his half- century in the morning but could not make it big after being cleaned up by Gamage (2/59) with a superb in-cutter.
Perera broke the partnership as the tourists successfully used a review to overturn the decision of Joel Wilson who stood in for indisposed Richard Kettleborough.
Jadeja was trapped in line but was given not out by the umpire as it seemed that the ball might have nicked the bat first but the review made it clear that there was pad first and the lefthander had to walk back to the pavillion.
Two balls later, Saha got out with a faint edge which was taken by Angelo Mathews at the first slip as India reviewed unsuccessfully.
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