The opening batter's chanceless unbeaten 146 off 238 balls, featuring 18 fours, on Thursday followed his career-best 187 in the drawn first Test at Galle last week.
Nissanka and Dinesh Chanidmal ground down the Bangladesh bowlers with their 194-run second-wicket stand.
Chandimal was seven runs from a century, 93 off 153 balls, when he tried to reverse sweep Nayeem Hasan and gloved an easy catch to wicketkeeper Litton Das in fading light.
Bangladesh wasted a review when they went for a lbw referral against nightwatchman Prabath Jayasuriya, who will resume on five.
Nissanka and Lahiru Udara gave Sri Lanka a brisk start of 88 before Taijul Islam broke through soon after lunch.
Udara made a brisk 40 off 65 balls but stayed in his crease against the left-armer's straight delivery and Bangladesh successfully reviewed.
Fast bowler Nahid Rana was wayward in his short spells despite bowling consistently at 144 kph, and the tall pacer's ploy of challenging Nissanka and Chandimal with bouncers also proved ineffective.
Chandimal successfully overturned a lbw decision on 30 before Nissanka raised his fourth Test century off 167 balls with a backfoot-driven boundary against Rana shortly after tea.
It is his 11th 50-plus score in his 18th Test.
Chandimal also opened up late in the last session with reverse sweeps as both batters used their feet well against the spinners and punished the loose balls from the quicks.
Earlier, Bangladesh resumed at 8-220 and lost the last two wickets after adding 27 more runs.
Left-arm spinner Sonal Dinusha, on debut, had the best bowling figures for Sri Lanka of 3-22, and fast bowler Asitha Fernando returned 3-51.
7°C