Bangladesh are currently 0-1 down in the three-match series, following their seven-wicket defeat in the first game.
Shamim Patwari made 26 ball-48 and Towhid Hridoy added 31 to help Liton in
setting the good target for Sri Lanka after a limping start that saw them reduced to seven for two in two overs.
Nuwan Thushara rattled the stump of Parvez Hossain Emon for duck in the third ball of the innings after Sri Lanka sent Bangladesh into bat first.
Binura Fernando who registered his career-best 3-31 in four overs, got into the act in the second over, having dismissed Tanzid Hasan Tamim for 5.
Liton and Hridoy then steadied the ship with the captain particularly in supreme touch, keeping the Lankan bowlers at bay.
They added 69-run for the third wicket before Fernando baffled Hridoy with a cutter. Three balls later, he struck again to get the better of Mehidy Hasan Miraz for 1 as Bangladesh further slumped to 78-4 in 12th over.
As it looked they would crumble under pressure again, Patwari joined Liton to help the side gain the momentum.
Their plan to counterattack instead of going for cautious approach after losing some wickets in quick succession paid the rich dividends.
Liton, however, reached his 12th T20 fifty, by hitting Maheesh Theekshana a six over the long-off. He then went for further carnage before Theekshana removed him after he struck one four and five sixes in his innings.
Shamim Patwari then drove the side closer to 180-run mark but fell two runs short of his fifty after being trapped run out in the last over, reports BSS.