Seamer Mustafizur Rahman and spinner Shakib Al Hasan picked up three wickets apiece to help Bangladesh reduce Sri Lanka to 8-268 in their second innings for a lead of 139 on the fourth day of the second Test.
The hosts, who conceded a first-innings lead of 129, appeared to be in big trouble in their second dig despite opener Dimuth Karunaratne's fine 126, his fifth Test hundred.
Sri Lanka were reduced to 6-190 at one point but fought back with useful partnerships from the lower order to boost their hopes of a whitewash in the two-match series.
Dilruwan Perera was unbeaten on 26 with Suranga Lakmal 16 not out and the pair have already added 30 for the ninth wicket to dampen Bangladesh's hopes of a maiden win against Sri Lanka in their 100th test.
Offspinner Mehedi Hasan struck with his first ball of the day to dismiss Upul Tharanga for 26 and break Sri Lanka's flourishing opening partnership after they had resumed on 0-54.
Karunaratne and Kusal Mendis (36) added 86 for the second wicket as Sri Lanka stayed on course to set Bangladesh a challenging target to chase on the final day.
Mustafizur and Shakib brought Bangladesh back into the match by inducing a mini collapse which saw the hosts lose 5-47.
Karunaratne and Perera then added 27 for the seventh wicket before the former became Shakib's (3-61) third scalp of the innings.
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