Hridoy struck an unbeaten 242 in the first innings, also the 25-year-old's maiden Test hundred, as the hosts recovered to post 386 all out in reply to the Windies' score of 356.
West Indies, with a 30-run deficit, then hit back strongly in the second innings to amass 398-6 declared with number 3 Kavem Hodge top-scoring with 142 while debutant Kevin Wickham hit 78.
With the declaration coming in teh first session on the final day, Bangladesh needed 369 runs to win if they wanted to square the two-match series.
The home side then slipped to 40-2 but Hridoy once again stood up with an enterprising 82 to become teh first player from his country to score mire than 300 runs in a Test match.
Mushfiqur Rahim contributed 49, and in the process became the first Bangladesh player to reach 7000 runs in Test cricket, as the hosts reached 184-4 before bad light brought an early end to proceedings.
West Indies claimed the series 1-0 following an eight-wicket victory in the first Test in Mirpur.
West Indies captain Roston Chase lauded his Test team for "going in the right direction as a unit" after going the entire calendar year without losing a Test series following their win in Bangladesh.
West Indies took a 1-0 lead in the two-match Test series in Bangladesh after wrapping up comfortable eight-wicket victory when chasing a target of 170 on the fourth day in Mirpur on Saturday.
Bangladesh have recalled seamer Taskin Ahmed into the squad ahead of the first Test against West Indies that starts in Mirpur on Wednesday.
Darren Sammy believes West Indies have taken a significant step forward after holding India to a 2-2 T20I series draw, with the head coach encouraged by the return of his team's confidence and trademark swagger.
