Kumar Sangakkara led the way with a captain's knock of 75, Thilan Samaraweera was unbeaten on 65 when bad light stopped play, and Mahela Jayawardene was out for 56 to a disputable lbw decision.
Anjelo Mathews was with Samaraweera at stumps on 26 not out.
India star Sachin Tendulkar became the most capped test cricketer when he started his 169th match, surpassing former Australia captain Steve Waugh's record of 168.
The 37-year-old Tendulkar, who made his test debut at 16, holds most of the game's major batting records.
After Sangakkara won the toss and elected to bat on a pitch that provided some movement, opener Tharanga Paranavitana was dismissed for 8 in the fourth over, caught behind by Mahendra Singh Dhoni off seamer Ishant Sharma.
Tillakaratne Dilshan put on 87 runs for the second wicket with Sangakkara before being run out for 41 at the stroke of lunch at 102-2.
After lunch, Sangakkara was caught by Virender Sehwag at long-off to a delivery from left-arm spinner Pragyan Ojha at 157-3 after facing 114 balls and hitting five boundaries and two sixes.
Sri Lanka went to tea on 194-3 and scored 99 runs in the final session.
Jayawardene was out to Ojha when he stretched far forward defensively and the ball hit high on the front pad.
However, television replays suggested the ball could have bounced higher than the stumps.
Jayawardene lasted 154 balls and hit only three fours for his 35th half-century.
Samaraweera has so far met 143 deliveries and hit six boundaries for his third half-century of the series.
Ojha has returned the best bowling figures for India with 2-78.
India retained Suresh Raina, who scored a century on debut last week, at the expense of Yuvraj Singh but lost the services of regular opener Gautam Gambhir and leading spin bowler Harbhajan Singh to injuries.
Murali Vijay will open the batting with Sehwag while legspinner Amit Mishra replaces Harbhajan.
Sri Lanka has been boosted by the return of seamer Lasith Malinga, who missed the second Test because of injury.
Chanaka Welegedara adds variety to the attack with his left-arm seam bowling.
Dammika Prasad and Dilhara Fernando were dropped.
Sri Lanka leads the series 1-0 after winning the first Test in Galle by 10 wickets. India must win this match to avoid losing a third series in Sri Lanka since 2001.
