Kasun Rajitha claimed 5-56 as Sri Lanka bowled Bangladesh out for 182 in its second innings on March 25 to clinch a 328-run victory in the first Test.
Rajitha, who returned 3-56 in the first innings, finished with career-best match figures of 8-112 in a Test match.
Mominul Haque played a lonely defiant innings for the hosts, stranded on 87 from 148 deliveries when the final wicket fell in the middle session on Day 4. His innings contained 12 boundaries and a six.
Bangladesh was set an improbable 511-run victory target after Sri Lanka rode on centuries in each innings from Kamindu Mendis and skipper Dhananjaya de Silva.
Sri Lanka made early inroads in Monday's morning session when Rajitha trapped Taijul Islam lbw for six in the second over after Bangladesh had resumed at 47 for five.
Mominul and Mehidy Hasan combined for a 66-run seventh-wicket stand, but Rajitha struck again to break up the partnership. Mehidy scored 33 from 50 deliveries before he played an expansive drive and got a thick outside edge.
Mominul also had a 47-run partnership with Shoriful Islam (12) for the eighth wicket, which only reduced the margin of the defeat.
Rajitha broke the partnership when he took a return catch to dismiss Shoriful. With his next delivery, he had Khaled Ahmed caught by Kusal Mendis for a duck to complete the second five-wicket haul in his test career.
Kumara, who returned figures of 2-39, ended Bangladesh's innings by dismissing Nahid Rana for a duck.
Vishwa Fernando couldn't add to his three-wicket haul from Day 3 and finished with figures of 3-36 from 15 overs.
After recovering from an early batting collapse at the start of the match, Sri Lanka posted 280 in the first innings with de Silva and Mendis each scoring 102.
After dismissing Bangladesh for 188, de Silva (108) and Kamindu (164) again hit centuries as Sri Lanka reached 418 in its second innings to set up victory. (AP) AYG
