The match was a poor advertisement for Test cricket in which 1,478 runs were scored for the loss of just 17 wickets on a flat pitch that offered no assistance to the bowlers.
There were five three-figure knocks over the five days, two of them double-centuries by Sangakkara and Sachin Tendulkar, besides a 99 from Indian opener Virender Sehwag.
Sri Lanka now head for the final Test at the P. Sara Oval from Tuesday enjoying a 1-0 lead in the series after winning the first match in Galle by 10 wickets.
India's last-wicket pair of Ishant Sharma and Pragyan Ojha, who resumed at the overnight score of 669-9, batted until 20 minutes before lunch to put on a partnership of 39 runs.
Sharma finally fell for 27, caught in the gully region off fast bowler Dilhara Fernando, leaving Ojha unbeaten on 18.
All four frontline Sri Lankan bowlers conceded more than 100 runs in India's innings, with debutant off-spinner Suraj Randiv going for 2-222 from 73 overs.
Unorthodox spinner Ajantha Mendis finished with 4-172, fast bowler Dilhara Fernando claimed 1-116 and seamer Dammika Prasad went for 0-101.
Part-time spinner Tillakaratne Dilshan was the only bowler to contain the Indians with figures of 3-56 from 27 overs.
India's innings was marked by Sachin Tendulkar's 203, his fifth double-century, while debutant Suresh Raina made 120 and skipper Mahendra Singh Dhoni hit 76.
Sangakkara had top-scored in Sri Lanka's first innings with 219, while opener Tharanga Paranavitana (100) and Mahela Jayawardene (174) hit centuries.