Bangladesh, boosted by a resolute knock of 91 by opener Shahriar Nafees, scored 301-7 after electing to bat first on a good batting pitch on Friday.
Kenya were bowled out for 170 in reply with left-arm seamer Syed Rasel ripping through their top-order to finish with 3-31.
Nafees struck 11 boundaries off 112 balls and was involved in two useful stands of 92 with Javed Omar (28) for the opening wicket and 76 with Aftab Ahmed (62) for the second.
Mohammad Rafique (36) and Mashrafe Mortaza (44 not out) then inflated the total with brisk knocks.
Left-handed Rafique struck three fours and a six off 25 balls while Mortaza smashed five fours and three sixes off just 16 deliveries.
For Kenya, young Tanmay Mishra top-scored with 43 off 82 deliveries, while Otieno Suji chipped in with 33 runs.
Bangladesh's previous highest total was 272-8 against Zimbabwe in Harare in 2001.