Asitha rips through Bangladesh as Sri Lanka win Test series
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"We knew we needed a couple of wickets to go our way," said Sri Lanka skipper Dimuth Karunaratne.
"The fast bowlers did the job for us, both in the first innings as well as the second."
Oshada Fernando sealed the devastating win with an unbeaten 21 in three overs.
Play had resumed on the fifth and final day with the hosts at a precarious 34-4 and Sri Lanka upped the pressure when Kasun Rajitha bowled Mushfiqur Rahim for 23 in the eighth over.
Shakib Al Hasan and Liton Das both hit fifties in a 110-run stand and held on through the first session with a mix of caution and aggression.
Shakib's counter-attack saw him hit Rajitha for three fours in one over, forcing Sri Lanka to widen their field set-up, while Liton played an anchor role after resuming on one overnight.
Liton was given out caught behind off Rajitha on nine as he attempted to flick a ball going down the leg, but survived on review.
It was the fourth caught behind decision overturned in the match, all given by West Indies umpire Joel Wilson.
He took the scalps of both Liton and Shakib soon after the break, claiming four of the last five wickets after dispatching openers Mahmudul Hasan Joy and Tamim Iqbal the previous day.
"A disappointing performance," said Bangladesh captain Mominul Haque.
"They put us under pressure with the new ball, we'll have to handle it better next time," he added.
The first Test in Chittagong ended in a draw.
Sri Lanka first innings 506 (Mathews 145, Chandimal 124; Shakib 5-96, Ebadot 4-148)
Bangladesh second innings (overnight 4-34)
Mahmudul Hasan c Mendis b Fernando 15
Tamim Iqbal c Mendis b Fernando 0
Najmul Hossain run out 2
Mominul Haque c Dickwella b Rajitha 0
Mushfiqur Rahim b Rajitha 23
Liton Das c&b Fernando 52
Shakib Al Hasan c Dickwella b Fernando 58
Mosaddek Hossain lbw b Mendis 9
Taijul Islam lbw b Fernando 1
Ebadot Hossain not out 0
Khaled Ahmed b Fernando 0
Extras (lb 1, nb2, w6) 9
Total (all out; 55.3 overs) 169
Fall of wickets: 1-15 (Tamim), 2-19 (Najmul), 3-19 (Mominul), 4-23 (Mahmudul), 5-53 (Rahim), 6-156 (Das), 7-163 (Shakib), 8-169 (Mosaddek), 9-169 (Taijul), 10-169 (Khaled Ahmed, 55.3 ov)
Bowling: Rajitha 12-5-40-2 (nb1, w1), Fernando 17.3-5-51-6 (nb1, w1), Jayawickrama 13-0-47-0, Mendis 11-2-20-1, de Silva 2-0-10-0
Sri Lanka second innings
Oshada Fernando 21
Dimuth Karunaratne 7
Extras (b1) 1
Total (3 overs) 29
Yet to bat: Kusal Mendis, Angelo Mathews, Dhananjaya de Silva, Dinesh Chandimal, Niroshan Dickwella, Ramesh Mendis, Praveen Jayawickrama, Kasun Rajitha, Asitha Fernando
Bowling: Taijul 1-0-16-0, Shakib 1-0-7-0, Ebadot 1-0-5-0
Result: Sri Lanka win by 10 wickets
Umpires: Joel Wilson (WIS), Sharfuddoula (BAN)
TV umpire: Richard Kettleborough (ENG)
Match referee: Chris Broad (ENG)