Former captain Angelo Mathews led Sri Lanka with 87 off 90 balls, guiding the side to 294-8 before Dasun Shanaka backed his 30 off 14 with three wickets for 27 runs to complete the rout.
Bangladesh will play three One-Day Internationals on July 26, 28 and 31 at the Premadasa International Stadium in Colombo.
Tamim Iqbal was named interim captain for the upcoming Sri Lanka tour after regular skipper Mashrafe Mortaza was ruled out with a hamstring injury.
At least 49 people died in attacks on two mosques in Christchurch during Friday prayers.
Mehidy Hasan's career best 4-29 helped Bangladesh restrict the Windies to 198-8 in 50 overs.
Tamim Iqbal has not played since injuring his wrist during the Asia Cup opener against Sri Lanka in September.
Virat Kohli has influenced many young cricketers with his batting and Tamim Iqbal is one of them.
Tamim Iqbal suffered an injury on the wrist in the second over of Bangladesh's innings against Sri Lanka when he was hit by a short ball from Suranga Lakmal.
Tamim Iqbal, who suffered the injury in the second over of Bangladesh's innings, is likely to be out of action for at least six weeks.
With the win, Bangladesh kept the series alive and also ended a five-match losing streak in T20Is going back to the final of the tri-nation series against India last March.
Man-of-the-Match Tamim blasted an unbeaten 130, the highest by a Bangladeshi in ODIs against the West Indies, while Shakib weighed in with 97 a second-wicket partnership of 207.
Mushfiqur Rahim scored a match-winning half-century as Bangladesh pulled off a memorable chase to stun Sri Lanka by five wickets in their Nidahas Trophy Twenty20 International match at R Premadasa Stadium in Colombo on Saturday.
Sri Lanka spinners led by Rangana Herath took three crucial wickets late in day four to leave Bangladesh with an uphill task of saving the opening Test in Chittagong on Saturday.
Tamim Iqbal smashed 84 as Bangladesh hit 320 and then inflicted further misery on Sri Lanka to claim their biggest win in one-day cricket on Friday.
Opener Tamim Iqbal struck an unbeaten half-century to guide Bangladesh to an eight-wicket win over Zimbabwe in the opening match of a tri-nation one-day international tournament in Dhaka on Monday.
Bangladesh were 127 for three at the close, still trailing by 369 runs after South Africa declared their first innings on 496 for three.
World Eleven side landed in Lahore in the wee hours on Monday for a Twenty20 series against the hosts.
According to ICC, Tamim was charged by match officials after he objected to the regular changing of gloves by an Australian batsmen.
