The world's leading wicket-taker grabbed 5-63 in the first innings as India were forced to follow on after being shot out for 276 on the fourth day in reply to Sri Lanka's 520-8 declared.
Sling-arm fast bowler Lasith Malinga then claimed three wickets to leave the tourists' second innings tottering at 181-5 at stumps, still 63 runs away from avoiding an innings defeat.
India, the top-ranked Test side, lost 12 wickets during the day on a wicket that took only slow turn at the Galle International Stadium.
Muralitharan, who dismissed Yuvraj Singh with the last ball of the day, will return for his final day in Test cricket on Thursday two short of the 800-wicket mark as Sri Lanka press for the lead in the three-match series.
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Batting superstar Sachin Tendulkar hit a defiant 84, sharing a third-wicket partnership of 119 with Rahul Dravid (44) after India were reduced to 42-2.
But Malinga, gaining appreciable reverse swing in the final hour, sent back the veteran pair in the space of si