Pace spearhead Zaheer Khan took 5-72 as Sri Lanka, trailing by 333 runs on the first innings, were shot out for 309 in their second knock 35 minutes into the fifth day's play at the Brabourne stadium.
The 2-0 scoreline lifted India to the top of the official Test rankings with 124 rating points, two more than previous leaders South Africa.
Sri Lanka slipped from second place to fourth with 115 points, one behind Australia (116).
About 10,000 home fans cheered lustily as the Indian players and the support staff, led by the team's South African coach Gary Kirsten, hugged each other after the fall of the last wicket.
Senior pro Sachin Tendulkar, the world's leading batsman in Test and one-day cricket, was ecstatic as he spoke to television commentators soon after the match.
buy xifaxan online buy xifaxan online no prescription
"It is fantastic to be the number one Test team," said Tendulkar, 36, who completed 20 years in international cricket at the start of this series.
"I have been waiting a long time to get to this p