The off spinner, 38, had last man Pragyan Ojha caught at slip by Mahela Jayawardene to terminate India's second innings after lunch on the final day of the first Test at the Galle International Stadium.
Muralitharan, who has more Test and one day (515) wickets than any bowler in history, will retire from Test cricket after the match.
India, who were made to follow on 244 runs behind, were all out for 338 in their second knock. Sri Lanka need 95 to win the Test and take the lead in the three match series.
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