India captured the wickets of Tillakaratne Dilshan for 14 and Tharanga Paranavitana for 34 after the openers had put on a stand of 50 and rounded off a good session when part-time bowler Virender Sehwag trapped Mahela Jayawardene for five.
Dilshan was caught at midwicket as he attempted a pull off Abhimanyu Mithun and miscued the shot and Paranavitana edged a catch to second slip off Harbhajan Singh.
Kumar Sangakkara was unbeaten on 30 and Thilan Samaraweera on nought not out.
India batted for a further 100 minutes on the fifth morning before Sri Lanka finally dismissed the last man after the tourists had amassed 707 runs, the highest total ever made by a visiting team.
India's tenth-wicket pair proved just how docile the pitch was when they batted without discomfort, adding 39 runs off 164 balls before Dilhara Fernando finally ended their resistance when he had Ishant Sharma caught at gully by Kumar Sangakkara for 27.
Pragjyan Ojha was left unbeaten on 18 as India forged a 65-run lead over the hosts, who scored 642-4 declared in their first innings.
Sri Lanka lead the three-match series 1-0 after their ten-wicket win at Galle last week.
(Editing by Clare Fallon)
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