Opener Lendl Simmons made a 49-ball 44, while Kirk Edwards (28 not out) and Darren Bravo (24 not out) were the unbeaten batsmen when play was called off with 15 overs remaining.
The hosts declared their second innings closed at their tea total of 119-3, with left-handed Shahriar Nafees (50) scoring his sixth Test half-century with the help of eight fours.
Openers Imrul Kayes (13) and Tamim Iqbal (37) were the other batsmen dismissed in the second session.
Seamers Darren Sammy and Ravi Rampaul, and spinner Marlon Samuels each took one wicket.
Debutant Elias Sunny became the third Bangladeshi to bag six wickets in an innings on debut in the morning session as the West Indies were bowled out for 244 in their first innings in reply to Bangladesh’s 350-9 declared.
It is to be mentioned that no play was possible due to rain on Saturday and Sunday.
The second and final Test starts in Dhaka on October 29.