Australia's Chappell brothers, Greg and Ian, achieved the feat against New Zealand in March 1974, before Misbah-ul-Haq and Azhar Ali emulated it against Australia in Abu Dhabi in 2014.
The pair, who had put together a 202-run partnership in Sri Lanka's first innings score of 280, added 173 runs this time around – on their way to becoming the third and fourth Sri Lankans to score centuries in both innings against Bangladesh.
Mehdi Hasan Miraz broke their partnership, before finishing with 4-74 for Bangladesh.