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The 22-year-old right-handed batsman was unbeaten on 56 and with him Darren Bravo was batting on 42 as the visitors now lead by 95 runs with a draw the most likely result on an unhelpful pitch for bowlers at Shere Bangla stadium.
Bangladesh made 556 runs in their first innings to take a slender 29-run lead over the West Indies first knock of 527-4 declared.
Powell and Bravo have so far added 104 runs for the unfinished second wicket stand after Chris Gayle failed for a second time, caught behind off paceman Rubel Hossain for 19.
Earlier, Nasir Hossain missed his maiden hundred by just four runs but still helped Bangladesh overhaul the West Indian total.
The 20-year-old Nasir, playing only his fifth Test, hitfour sixes and six boundaries during his fiery 136-ball knock -- improving on his previous best of 79 against Pakistan at the same venue last year.
Resuming at 455-6, Bangladesh were guided towards the West Indian total by a solid 121-run stand for the seventh wicket between Nasir and Mohammad Mahmudullah (62) before Sunil Narine gave the West Indies the much-needed wicket.
Narine, who went wicket-less on the third day, dismissed Mahmudullah, caught by Powell and then four runs later had Sohag Gazi bowled for four.
Sensing Bangladesh would fell short of the West Indian total, Nasir took the attack to himself by adding 61 for the ninth wicket with Shahadat Hossain (13) and during the stand also took his team into the lead.
Nasir hit two sixes off Veerasammy Permaul and one off Narine to enter 90s but was caught off a miscued lofted shot off paceman Tino Best.
Paceman Ravi Rampaul and Narine finished with three wickets apiece.