The off-spinner took his career tally to 797 wickets as India were shot out for 276 in reply to Sri Lanka's 520-8 declared after lunch on the fourth day.
India, trailing by 244 runs, went to tea struggling at 68-2 in their second knock with Rahul Dravid unbeaten on 12 and Sachin Tendulkar on 21.
Fast bowler Lasith Malinga, who had removed Gautam Gambhir second ball in the first innings, dismissed the left-hand opener with his third delivery for no score.
First-innings centurion Virender Sehwag hit a breezy 31 off 30 balls before he was superbly caught at gully by Mahela Jayawardene off left-arm seamer Chanaka Welegedara.
It was the 67th time Muralitharan had claimed five wickets or more in a Test innings, way ahead of second-placed Australian spinner Shane Warne, who did it on 37 occasions.
The world's leading wicket-taker, who retires from Test cricket aged 38 after the match, followed up the dismissal of Tendulkar for eight on Tuesday with four more scalps.
Mura