Bangladesh, set a target of 467 runs to record a series-levelling victory, were 271-3 in their second innings when stumps were drawn on the fifth day at the Zahur Ahmed Chowdhury stadium.
Mominul Haque remained unbeaten on 100 and Shakib Al Hasan was on 43, the pair having added 120 runs for the fourth wicket.
Sri Lanka had won the first Test by an innings and 248 runs in Dhaka last week.
It was only the second draw in 16 Tests between the two countries, with Sri Lanka having won the other 14 matches, eight of them by an innings margin.
Bangladesh, who languish at the bottom of the Test rankings at number 10 -- lower than unfancied Zimbabwe -- have lost 68 of their 83 Tests since gaining full status in 2000 and won only four.