Wriddhiman Saha was unbeaten on 56 and Ishant Sharma was on two after India resumed at their overnight score of 319-6.
Opener Lokesh Rahul top-scored with 108, skipper Virat Kohli made 78 and Rohit Sharma hit 79 on the first day after India won the toss and elected to bat.
Sri Lanka lead the three-match series, having won the first Test in Galle by 63 runs.