West Indies captain Darren Sammy said his team's self-belief never wavered despite being led on first innings by Bangladesh in the first Test, which finished yesterday.
The Caribbean side pulled off a convincing 77-run victory to take a 1-0 lead in the two-match series, after Bangladesh had been set 245 to win at the Shere Bangla Stadium.
"Credit must go to them for the way they came out and played this match. They batted really well and had a game plan and executed it well," Sammy told reporters.
"We always had a belief that we could get a victory, and no matter how hard they fought, we felt we could come out on top.
"I know they will take a lot of positives from this game, but so will we. It leaves the series wide open and we have seen they are not a side that will roll over, so we expect a bigger fight and hopefully we can again be victorious."
West Indies piled up 527 for four declared in their first innings after winning the toss and batting, but Bangladesh responded strongly with 556 to take a 29-run lead.
The hosts then produced a superb effort to dismiss West Indies for 273 in their second innings, but struggled in their run chase as fast bowler Tino Best routed them with figures of five for 24.
"It was a difficult pitch for the bowlers—over 1,000 runs were scored in the first two innings," Sammy pointed out.
"The effort from Tino, running in hard and putting the ball consistently in the right areas, and getting his first five-wicket haul in Tests was special."
He added: "We knew we needed to get 10 wickets to win the match, but we saw how the pitch behaved the previous evening and in the morning session—there was something in it for the spinners and our fast bowlers are much quicker.
"We backed our bowlers to put the ball in the right areas, and once we were patient, we could get wickets."
West Indies face Bangladesh in the second Test starting on Wednesday, and Sammy said the victory augurs well for his side's already high confidence.
"We have said from the beginning, we had a lot of respect for Bangladesh and we were not going to take them lightly and we didn't," he noted.
"Had we taken them for granted, the result of the first innings total would have caused panic in the dressing room."
He continued: "But to see that we battled our way throughout the Test and came out victorious will definitely be a boost to the confidence that we already had coming out of the ICC World Twenty20 Tournament.
"It will also help improve the attitudes of players whenever we take the field and face a difficult task."