The Bangladesh skipper Mominul Haque fell after a well compiled 127 runs.
Earlier, Lahiru Kumara striked to end mammoth Najmul Hossain Shanto-Mominul Haque stand after lunch. Shanto became caught out at 163 runs.
He picked up 163 runs off 378 balls with 17 fours and one six.
The pair added 226 runs for their unbroken third-wicket stand, having batted together for 79.3 overs
Bangladesh score: (145 ov) 440/4
Skipper Mominul Haque hit century against Sri Lanka in the first innings of a two-match Test series at Pallekelle International Cricket Stadium in Kandy on Thursday.
The century is the first outside of the country.
Najmul Hossain Shanto and skipper Mominul Haque on Thursday morning started batting for a big score.
Bangladesh ended the opening day on Wednesday for 302 runs losing two wickets.