Chasing 250 for a win, Hope, opening the innings, smashed three sixes and eight fours in his 145-ball 109 not out to help West Indies overhauled the target, scoring 253 for 5 in 48.4 overs.
Steve Smith and Pat Cummins continue to top the ranking charts following their superb performances in the fourth Ashes Test.
Under Gulbadin Naib, Afghanistan lost all nine of their World Cup matches in England.
The visitors -- playing only their third Test in history -- reached 237-8 at stumps on the third day, setting a huge target for Bangladesh by taking an overall lead of 374 runs.
Afghanistan were 156-4 at tea on the third day, extending their 137-run first innings lead to 293 runs.
Captain Rashid Khan smashed his maiden Test half-century as Afghanistan were bowled out for 342 runs.
Afghanistan were 271 for five at stumps with Afghan and Afsar Zazai, on 35, putting together a 74-run partnership in the final session of play.
Shah made 102 and put on a crucial 120-run fourth-wicket stand with Asghar Afghan, batting on 88, to counter the Bangladesh spin attack.
Before the World Cup, Rahmat Shah was appointed Test captain while Gulbadin Naib emerged a surprise choice for ODI captaincy. Rashid himself was named the T20 captain.
Teenage paceman Shaheen Shah Afridi took four wickets as Pakistan limited Afghanistan to 227 for nine in their World Cup match.