The West Indians erased the bad memories of the previous day, when they completed an efficient 23-run victory in the rain-shortened second one-day international over Bangladesh on Sunday.
Chasing 125 to win, Bangladesh were restricted to 101 for eight from their allotment of overs, after overnight and persistent morning showers forced a late start and reduced the match to 25 overs-a-side.
West Indies now take an unbeatable 2-0 lead in the three-match series with the last one-day international scheduled for the Queen's Park Stadium in St. George's, Grenada, on Wednesday.
Chasing 145 to win, West Indies scrambled to a one-wicket victory with 20 balls to spare in the opening match on Saturday.
"I think our bowlers bowled pretty well for us and there is no one individual that I could pinpoint, it was a total team effort," acting West Indies captain Ramnaresh Sarwan said.
"I thought we were brilliant in the field, especially Dwayne Smith, and this is an area of our game that we are trying to improve on," he added.
"We have set ourselves some goals for this series and, hopefully, we can go to Grenada and continue the hard work and win there too."
Smith, named Man of the Match, curbed his natural instincts to collect his highest one-day international score, as West Indies were restricted to 124 for seven from their allotment of 25 overs.
Smith hit two fours and two sixes in a run-a-ball, undefeated 62 and was given a reprieve on 25 when Manjural Islam Rana dropped a head-high return chance.
Tapash Baisya snatched four late wickets for 16 runs from five overs to be the pick of the Bangladesh bowlers and claim the best bowling figures by a bowler from his country in one-day cricket
"In the matches I have played previously, I have gotten a few starts without carrying on, but I had the opportunity to bat at three this time, grabbed it with both hands, and I am happy," Smith said.
"I still have to work hard because cricket is not an easy game. Next match, I start with zero, so I have to keep working on the weaknesses I have and improve on my scores in the future."
Once Fidel Edwards removed Mohammad Ashraful and Bangladesh captain Habibul Bashar in the space of five balls in the third over, it was always going to be an uphill struggle for the visitors.
Hannan Sarkar, the only change to the previous day's line-up, was the Bangladesh top scorer with 36 from 55 balls and Manjural, batting at seven, scored 33 not out from 43 balls to add some beef to the visitors' total.
Ian Bradshaw with three for 15 from five overs was the most successful West Indies bowler. Edwards took two for 19 and Dwayne Bravo two for 23 from their allotment of five overs.
"We did not bat well again," Bashar said.
"Our bowlers did the job, but we were short of some good batting to make the match more competitive.
"We are hoping that we can win in Grenada because it would be a morale booster for the Test series."
After the visitors decided to field in overcast to cloudy conditions, the West Indies batsmen struggled with their timing on a hard, but slow Arnos Vale pitch, and found it hard to gather runs in torrents against the medium-paced stuff of the Bangladeshis.
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