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.