The trio replaced Khaled Mashud, Shakib-Al Hasan and Abdur Razzak. Fast bowler Malinga and off-spinner Muralitharan grabbed four wickets each as Bangladesh, sent in to bat at the P.
Sara stadium, were dismissed in the first over after lunch off 25.
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2 overs.
Sri Lanka took a first innings lead of three runs by tea as they went into the break on 65-1 with Malinda Warnapura unbeaten on 36 and Kumar Sangakkara on nine.
Left-hander Michael Vandort was the batsman out, bowled by Mashrafe Mortaza for 14.
Bangladesh, thrashed by an innings and 234 runs in last week's first Test, fell below their previous lowest total of 86, also against Sri Lanka in 2005.
Malinga, 23, whose distinctive slinging action makes him a dangerous foe, created havoc in the rival ranks by scalping the first four wickets in a hostile opening spell.
The tourists were reduced to 22-4 within the first hour, before Muralitharan (4-14) and third seamer Dilhara Fernando (2-16) polished off the rest of the batting.