Sri Lanka were all out for 181 in their second innings after made to follow on.
A ruthless India completed a historic 3-0 whitewash in one of the most one-sided test series in recent times as they crushed Sri Lanka inside three days in the final test on Monday. It was India's first series clean sweep overseas.
Hardik Pandya was declared the player of the match while Shikhar Dhawan was adjudged the man of the series.
Off-spinner Ravichandran Ashwin and paceman Mohammed Shami shared seven wickets between them as the world's top-ranked side shot out Sri Lanka for 181 to win by an innings and 171 runs.
The beleaguered hosts, whose second innings ended shortly after the scheduled tea break, had been asked to follow on after managing 135 in their first innings in reply to India's 487.
Ashwin picked up 4-68 in the second innings while Shami finished with 3-32 in an inspired bowling performance by India, who triumphed both in Galle and Colombo inside four days.
"A good day, a good win for us. Very happy with the overall performance and it always feels nice to have convincing victories," India captain Virat Kohli said at the presentation ceremony.
"We are a young side. We look forward to playing test cricket, we look forward to playing with the same excitement. That's the only way you can be ruthless."
All-rounder Hardik Pandya, who scored his maiden test hundred on Sunday, was adjudged man-of-the-match while opener Shikhar Dhawan, a last minute replacement for Murali Vijay, was named player of the series.
Sri Lanka's highest partnership of 65 came between captain Dinesh Chandimal, who made 36, and former skipper Angelo Mathews (35) while wicketkeeper Niroshan Dickwella scored a fluent 41.
Their hopes of avoiding an innings loss rested on a solid start but Ashwin struck in his first over of the day to jolt the hosts.
The off-spinner sent back opener Dimuth Karunaratne for 16 after Sri Lanka had resumed on 19-1. The left-hander was caught by Ajinkya Rahane at slip after getting a thick edge to a turning delivery.
Nightwatchman Malinda Pushpakumara was caught behind off Shami who also dismissed Kusal Mendis for 12 to reduce the hosts to 38-4.
Left-arm wrist-spinner Kuldeep Yadav broke the stand between Chandimal and Mathews when he dismissed the former through a bat-pad catch at short leg.
Once Mathews was out leg before to Ashwin, India's win was merely a formality. "Our batting and bowling was below-par through the series," Chandimal said after his team's failure to make any of the tests last full five days.
"We have to be more patient and concentrate more."
The sides will now clash in five one-day internationals and a Twenty20 starting on Sunday.
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