Bangladesh off-spinner Nayeem Hasan took five wickets to halt Sri Lanka's first-innings charge as they were dismissed for 485 in the post-lunch session on the fourth day of the first Test in Galle on Friday.
Nayeem took 5-121 and was well supported by Hasan Mahmud, who finished with 3-74, giving the visitors a 10-run lead after they made 495 in their first innings.
With the pitch finally offering turn and bounce, Nayeem made the most of the conditions, the hosts having looked firmly in command at the end of day three.
Sri Lanka looked set for a useful lead after the first session of the fourth day, reaching 465-6 with Kamindu Mendis and Milan Rathnayake stitching a gritty 84-run stand for the seventh wicket.
But the hosts lost the momentum with a lower-order collapse after lunch.
The breakthrough came when Rathnayake, who had shown commendable defiance for his 39, was undone by a delivery from Mahmud that sneaked through off an inside edge.
Kamindu followed in the next over, falling to Nayeem's off-spin as the ball kicked off the surface and caught the left-hander by surprise.
Kamindu scored a composed 87 -- with eight fours and a six -- and fell just short of a third hundred against Bangladesh.
Sri Lanka's lower order folded within the next few overs with Nayeem removing debutant Tharindu Rathnayake for nought with a sharp off-break that went through the gate.
It reduced the hosts to 471-9, losing three wickets for just one run in 10 deliveries. Nayeem also removed Asitha Fernando (4) to close Sri Lanka's innings.
With the pitch crumbling, Sri Lanka's spinners will be in the game early but even a small Bangladesh score could be a challenging target in the fourth innings for the hosts.
The Galle cricket ground saw its last draw more than a decade ago, between both these sides in 2013.