Murali Vijay made 82 and Ajinkya Rahane was unbeaten on 82, the pair having put on 140 for the second wicket after Lokesh Rahul had been dismissed off the fifth ball on Saturday.
Rohit Sharma was the other batsman at the crease on two.
Sri Lanka made 306 in their first innings in reply to India's 393.
Sri Lanka lead the three-match series, having won the first Test in Galle by 63 runs.