West Indies need 193 runs more to win the match in eight sessions with six wickets remaining in hand.
Shimron Hetmyer [5* off 3b; 1x4] and Sunil Ambris [0* off1b] were at the crease in the fifth wicket at lunch.
Taijul conceded no runs in five balls for his two wickets –skipper Kraigg Brathwaite [8] and Roston Chase – both by lbw.
Shakib made the first breakthrough, dismissing Kieran Powell on 5/1 in 2.4 overs before got Shai Hope on 11/2 in 4.5 overs. Powell and Hope both were caught behind by Mushfiqur Rahim.
Earlier, Bangladesh posted a 203-run lead adding another 70 with their overnight total of 55 for five. The hosts were all out for 125 runs.
Mahmudullah Riyad top-scored 31 off 46 balls, including one boundary and one six. He was caught by Shai Hope off-spinner Devendra Bishoo. .
Apart from sending off Mahmudullah, Bishoo dismissed overnight Mehidy Hasan Miraz [18 off 35b; 3x4] and debut Nayeem Hasan [5].
Another overnight batsman Mushfiqur Rahim [19 off 39b; 1x4] played 10 balls and added 8 runs to his previous 11 before being bowled out by Shannon Gabriel at 69/6 in 18.5 overs.
Bangladesh’s last man spinner Taijul Islam was caught by Jomel Warrican off Roston Chase on his single digit.
Devendra Bishoo [4/26], Roston Chase[3/18], Jomel Warrican [2/43] and Shannon Gabriel[1/24] were the wicket-takers for the Windies.
Brief score:
Bangladesh 1st innings: 324/10 in 92.4 overs; Mominul Haque 120, Imrul Kayes 44, Taijul Islam 39*, Shakib Al Hasan 34, Nayeem Hasan 26, Mehidy Hasan Miraz 22, Mohammad Mithun 20, Jomel Warrican 4/62, Shannon Gabriel, 4/70, Kemar Roach [1/63, Devendra Bishoo 1/60.
Bangladesh 2nd Innings: 125/10 in 35.5 overs (overnight 55/5 in 17 overs); Mahmudullah Riyad 31, Mushfiqur Rahim 19, Mehidy Hasan Miraz 18, Mohammad Mithun17, Mominul Haque 12, Soumya Sarkar 11, Devendra Bishoo 4/26, Roston Chase 3/18, Jomel Warrican, 2/43, Shannon Gabriel 1/24.
West Indies 1st Innings: 246/10 in 64 overs; Shane Dowrich 63*, Shimron Hetmyer 63, Roston Chase 31, Sunil Ambris 19, K Powell 14, K Brathwaite13, Nyeem Hasan 5/61, Shakib Al Hasan 3/43.