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Both bowlers finished with four wickets each as Bangladesh, resuming their second innings at 233-5, were shot out for 254 within 30 minutes of the start of the fourth day's play at the Sinhalese Sports Club.
It was Sri Lanka's biggest victory over Bangladesh, surpassing the innings and 196-run win at the P. Sara stadium here in 2002.
Sri Lanka have now won all their eight Test matches against Bangladesh, five of them by an innings.
The Sri Lankans have been so dominant against the Test minnows that they have never required a fifth day to secure victory.
Four of the Tests have ended inside three days and the remaining four with a day to spare.
It was Bangladesh's 41st defeat in 47 matches since they gained Test status in 2000 with a lone win coming against struggling Zimbabwe.
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Five games have been drawn.
Fast bowler Malinga took three of the last five wickets and off-spinner Muralitharan claimed the other two as Sri Lanka made short work of Bangladesh on the fourth morning.