The duo fashioned an unbeaten 253-run sixth-wicket stand as Bangladesh reached 277 for five at stumps after choosing to bat at the Sher-e-Bangla National Cricket Stadium in Mirpur.
Sri Lanka seamers Kasun Rajitha (3-43) and Asitha Fernando (2-80) tore through the Bangladesh batting lineup by reducing them to 24 for five inside seven overs.
Despite the rollicking start, Mushfiqur and Litton made the most of their forms and dug deep to breeze through the rest of the day at 3.25 runs an over as the surface eventually became flat, offering little for the spinners.
Litton was the more adventurous of the two as he pulled, drove and lobbed the ball without hesitation. On 47, he top-edged Fernando to square leg where substitute Kamindu Mendis failed to latch on to the ball. That was the only real chance offered by the batters.
Litton was harsh on the bowlers erring on the length. He raced past the 80s and 90s to reach his second Test century. He laced his 221-ball innings with 16 boundaries and a six and kept the runs coming after reaching the personal milestone.
Mushfiqur - fresh from his century in Chattogram in the first Test - began with two boundaries in the first eight deliveries to get into the groove. He then steadied his innings and adopted an eye for bad balls, which Sri Lankan spinners threw in plenty.
The pair rarely missed out on scoring opportunities but was watchful with good deliveries. Halfway through the third session, Mushfiqur squared one up for his ninth century in the format, third against Sri Lanka. His 252-ball innings contained 13 boundaries.
Earlier, Rajitha set the morning collapse in motion with the second ball of the match as all the five batsmen failed to go past single-digit scores. He took out Mahmudul Hasan Joy (0) by going through his gates. He also castled Najmul Hossain Shanto (8) luring him into a drive and then trapped Shakib Al Hasan (0) leg before.
Fernando took out Bangladesh’s inform opener Tamim Iqbal (0) who sent a leading edge to point before a struggling Mominul Haque (9) poked at a length ball outside off for a thin edge back to the keeper and registered his sixth successive single-figure score.
Sri Lankan spinners, however, failed to pose any threat to the batters as the track is yet to offer any serious turn.
