Mahmudullah has played 24 one-dayers for Bangladesh
A superb bowling spell from Mahmudullah saw Bangladesh record only their second ever Test victory with a 95-run win against a weakened West Indies side.
Set 277 to win, the home side crumbled to 181 all out as the debutant off-spinner ripped through the batting order with 5-51 in St Vincent.
David Bernard (52 not out) was the only batsman to provide any resistance.
Earlier, Bangladesh lost their last five wickets for 23 runs to finish on 345 with Darren Sammy claiming 5-70.
The victory is Bangladesh's first overseas - their previous win came against Zimbabwe over four years ago in Chittagong - in 60 matches since their introduction to Test cricket nine years ago.
The victory was made the more remarkable considering captain and strike bowler Mashrafe Mortaza missed the West Indian innings with a knee injury, with vice-captain Shakib Al Hasan deputising in his absence.
"It was probably a blessing in disguise when we got bowled out (on Monday morning) which gave us more time," said Mortaza, skippering his first Test match since succeeding Mohammad Ashraful last month.
I thought we let ourselves down in the first innings
Captain Floyd Reifer
"We were looking to bat until lunch and get a lead of about 300 or more, but we lost our last five wickets quickly."
However, Bangladesh's achievement came against a second-string West Indies side missing 13 of its best players because of an ongoing contract dispute with the West Indies Cricket Board (WICB).
The board has insisted it will field the same squad - seven of whom made their debuts at Arnos Vale - if no settlement can be reached ahead of the second Test, which starts in Grenada on Friday.
The final day began promisingly for the home side as Sammy claimed three dismissals for his second Test five-wicket haul.
But with 80 overs to chase down 277 on a wearing wicket encouraging turn, the inexperienced West Indies batting line-up succumbed to Bangladesh's triple spin attack.
Openers Dale Richards and Omar Phillips each fell for 14 before captain Floyd Reifer became the first of Mahmudullah's five victims for 19.
Reduced to 85-5, Bernard found support in Sammy, but the vice-captain was dismissed by Shakib Al Hasan to leave the home side precariously placed at 119-6.
Despite reaching his second half century of the match, Bernard could not find adequate support as Bangladesh wrapped up their historic victory 40 minutes from the scheduled close.
"It is disappointing to lose but I think the guys, brought here the night before a Test, fought well," said 36-year-old stand-in skipper Reifer, who made his first international appearance in more than 10 years.
"I thought we let ourselves down in the first innings, when the batsmen did not capitalise on the starts that they got.
"Many of us got a start, but never really carried on. Young Omar Phillips scored 94, but I thought that a lot of other guys, including myself, got starts, and we never carried on to a big score."