The Sri Lankans scored 222 in its first innings after winning the toss and deciding to bat.
The first Test in Chittagong ended in a draw.
Dhaka: Sri Lankan spinners masterminded a fantastic 215-run win over Bangladesh on the third day of the second and final cricket Test to seal a 1-0 away series win at the Sher-e-Bangla National Stadium here on Saturday. However, their inconsistency with line and lengths and the lack of pressure meant that Roshen Silva was able to farm the strike easily, keeping Suranga Lakmal out of harm's way.
Dananjaya was the wrecker-in-chief with eight-wicket haul in the match and he was ably supported by experienced Rangana Herath (4/49).
Even when Lakmal faced the bowlers, Bangladesh allowed him to get off strike and make things easier for Sri Lanka as the ninth-wicket pair scored at a steady rate to stretch the lead.
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In their chase, Bangladesh lost Tamim Iqbal on the first ball of the second over for two, trapped in front when he missed one from Dilruwan Perera that didn't turn.
De Silva played an attacking 24-ball 28 before he was dismissed by a quicker delivery from left-arm spinner Taijul Islam.
The visitors were 8-200 at stumps, after taking a 112-run lead on the first innings. Our bowlers [only] did well in patches.
Pace bowler Mustafizur Rahman then removed Danushka Gunathilaka for 17 but Karunaratne remained.
Earlier, Sri Lanka added 26 runs to their overnight score before they were all out for 226 in their second innings to set up a mammoth target for Bangladesh.
The hosts appeared to have made a solid enough start as four of their top five, led by Mominul Haque (33), managed to reach double figures.