Skipper Virat Kohli was unbeaten on one and Rohit Sharma was on 14 after the tourists were reduced to 7-3 by the sixth over.
India made 312 in their first innings and Sri Lanka replied with 201 on a day in which 15 wickets fell at the Sinhalese Sports Club.
Sri Lanka won the opening Test in Galle by 63 runs and India drew level with a 278-run victory in the second match at the P. Sara Oval in Colombo last Monday.
