That left the home team still 127 runs adrift of Bangladesh, who had piled up a huge total of 495 all out earlier on Thursday.
On a featherbed surface, Nissanka produced an innings of sublime timing and poise, the sort that makes connoisseurs purr and opponents wince.
Nissanka, whose two previous Test hundreds had come overseas, finally notched his maiden century on home soil.
A double hundred looked inevitable but the second new ball brought about his downfall.
A touch too eager to assert, Nissanka offered a drive too early, left a gap between bat and pad, and was clean bowled by Hasan Mahmud.
Debutant Lahiru Udara, also looking assured during a brisk 29 off 34 balls, peppered the boundary with six well-timed fours before offering a return catch to Taijul Islam off a leading edge.
Dinesh Chandimal then stitched together a 157-run stand for the second wicket with Nissanka, his 54 also oozing class until a faint tickle down the leg side ended his stay.
Angelo Mathews, in his final Test, appeared in decent touch during a fluent 39 before falling to Mominul Haque, the part-time spinner luring an edge to the keeper.
"It was an honour to bat with Angelo," Nissanka said. "He is an amazing guy. He has done a lot for the game and has helped me out too."
Captain Dhananjaya de Silva (17no) and the versatile Kamindu Mendis (37no) then took Sri Lanka to the close of play with an unbroken 37-run partnership.
With more batting depth to come and time on their side – should the weather hold – Sri Lanka will fancy their chances of claiming a first-innings lead.
Earlier, Sri Lanka wrapped up the Bangladesh innings inside 15 minutes with Asitha Fernando taking 4-86.
Bangladesh's Australian fast-bowling coach Shaun Tait said: "Sri Lanka are a team that was competing for the WTC final six months ago. I think they batted really well.
"The pace bowlers missed a trick with the new ball. It would have been nice if they had taken a couple of wickets with the new ball.
"I think we would have taken our score at the start of the game. We got a good score. We can't ask much more than that from Bangladesh."
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