The Tigers, winning the toss, piled up a mammoth 322 for six in their 50 stipulated overs.
In reply, Grenada managed only 227 for nine.
Opener Tamim Iqbal scored the highest, 91, for the tourists. His 86-ball innings sparkled with 12 fours and two sixes.
The left hander built up a 88-run third wicket partnership with Shamsur Rahman (32), after a 56-run opening partnership with Anamul Haque (24), to lay a solid base for the tigers.
Mahmudullah added 78 before he was sent back off the final delivery. His quick-fire batting helped the visitors add 114 runs in the final 10 overs.
He smashed seven fours and three sixes in his 61-ball innings.
Mashrafe Bin Mortaza picked up three wickets, the highest for Bangladesh bowlers, while Al-Amin and Abdur Razzak picked up two each.