Dowrich added 92 runs for the sixth wicket with Shimron Hetmyer, who scored 63 off 47 balls.
Nayeem's first coach interestingly was Mominul Haque, who recalls the teenager bowling medium-pace.
Teenage Bangladesh off-spinner Nayeem Hasan became the youngest ever player to take five wickets on debut but West Indies' spinners matched him to restore parity in the first Test in Chittagong on Friday.
By stumps on day two in Chittagong, Bangladesh were 55/5 with a lead of 133 over West Indies.
Teenage off-spinner Nayeem Hasan became the youngest ever player to take five wickets on debut as Bangladesh bowled out the West Indies for 246 in the first Test in reply to the hosts' 324.
Hetymer's 42-ball fifty revived West Indies after they had lost half their side for 88 runs on day two in Chittagong.
Mehidy Hasan, the debutant offspinner Nayeem Hasan and Taijul Islam added 56 runs to Bangladesh's total after Shannon Gabriel's four wickets.
Bangladesh have drafted in the debutant offspinner Nayeem Hasam as one of four slow bowlers in the XI.
Taijul Islam and Mehidy Hasan Miraz have led Bangladesh's spin attack admirably in the absence of Shakib, feels the spin consultant.