Bangladesh lost wickets continuously.
Shahadat Hossain (eight) was caught by Kamindu Mendis at slip off Kumara's ball and Jayasuriya hit Mehdi Hasan (seven) in front.
Asitha Fernando ended Mominul's resistance before bowling Khalid Ahmed for one run and ending the innings.
Sri Lanka dominated Bangladesh in the first two days and scored 531 runs, the highest Test score without any batsman scoring a century.
Sri Lanka, which has never lost a Test series to Bangladesh, won the first Test in Sylhet by 328 runs.