Captain Shakib Al Hasan and Mahmudullah Riyad were unbeaten on 55 and 31 respectively.
Debutant opener Shadman Islam scored a gritty half-century hitting 76 off 199 balls before he was trapped leg-before by Devendra Bishoo.
Tigers went into the game without any recognised fast bowler as they dropped Mustafizur Rahman and replaced him with additional batsman Liton Das.
Wicketkeeper-batsman Mushfiqur overcame concerns about his fitness to be included in the side.
West Indies replaced suspended Shannon Gabriel with right-arm pacer Sherman Lewis.
The home side lead the two-Test series 1-0 thanks to their 64-run win in the opening Test in Chittagong.
Bangladesh first innings scorecard:
Shadman Islam lbw b Bishoo 76
Soumya Sarkar c Hope b Chase 19
Mominul Haque c Chase b Roach 29
Mohammad Mithun b Bishoo 29
Shakib Al Hasan not out 55
Mushfiqur Rahim b Lewis 14
Mahmudullah Riyad not out 31
Extras (b2, nb 4) 6
Total (five wickets; 90 overs) 259
To bat: Liton Das, Mehidy Hasan, Taijul Islam, Nayeem Hasan
Fall of wickets: 1-42 (Soumya), 2-87 (Mominul), 3-151 (Mithun), 4-161 (Shadman), 5-190 (Mushfiqur)
Bowling: Roach 15-1-38-1 (nb1), Lewis 12-1-35-1, Chase 21-0-61-1 Warrican 19-2-46-0, Bishoo 19-1-69-2 (nb3), Brathwaite 4-0-8-0
Umpires: Aleem Dar (PAK) Ruchira Palliyaguruge (SRI)
TV umpire: Richard Illingworth (ENG)
Match referee: Andy Pycroft (ZIM)