Sri Lanka established a 488-run first innings lead over Bangladesh on the second day of the first Test in Colombo before declaring shortly before stumps.
Having dismissed Bangladesh for 89, Sri Lanka made 577-6, with Michael Vandort (117) and Mahela Jayawardene (127) completing centuries before lunch.
Prasanna Jayawardene (120 not out) and Chaminda Vaas (100 not out) then weighed in with maiden Test tons.
Bangladesh were 3-0 at close and struggling to avoid a crushing defeat.
The left-handed Vandort, a late replacement for the injured Upul Tharanga, hit nine fours and three sixes in his innings.
Vandort, who resumed on his overnight score of 87, hit consecutive sixes off left-arm spinner Abdur Razzak to move to 99 and then clipped two runs to mid-wicket in the same over to reach his third Test century.
He put on 117 for the fourth wicket with Tillakaratne Dilshan before being caught via bat and pad off spinner Mohammad Rafique.
Bangladesh earned a fifth wicket when Dilshan was run out for 79 after Mahela Jayawardene had declined his call for a second run.
Skipper Jayawardene, who had retired hurt the previous day on 93 because of cramp, completed his 17th Test century before falling soon after lunch, punching Mashrafe Mortaza to point.
He became Sri Lanka's second-highest scorer with 6,416 runs in 86 Tests, fast closing on Sanath Jayasuriya's record tally of 6,791.
There was, however, no respite for the Bangladeshis as wicket-keeper Prasanna Jayawardene and Vaas put on 223, the best ever stand by a Sri Lanka seventh wicket pair in Tests.
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