Sri Lanka, needing 160 to win, were 1-103 in their second innings at tea on the penultimate day of the second and final Test against Bangladesh in Colombo on Tuesday.
Opener Tillakaratne Dilshan was unbeaten on 52 with Kumar Sangakkara 33 not out.
Bangladesh, trailing by 106 runs on the first innings, were dismissed for 265 in their second innings in the morning session.
Tamim Iqbal (59), Jahurul Islam (48) and skipper Mushfiqur Rahim (40) were the main scorers, while Sri Lankan left-arm spinner Rangana Herath finished with a career-best 7-89 on his 35th birthday.
The hosts on Monday were bowled out for 346 in their first innings in reply to Bangladesh’s 240. The opening Test in Galle ended in a draw.