Opener Omar struck a disciplined 64 and Ahmed got a stroke-filled 59 as the home side reached a target of 162 in just 23.5 overs on Monday to take an unassailable 2-0 lead in the four-match series.
Omar struck 11 fours in his 79-ball knock while Ahmed smashed nine fours and two sixes off 48 balls against the hapless visiting side, who got the lone wicket of opener Shahriaf Nafees (28).
Earlier, Kenya, who went down by 131 runs in the opening match in Bogra on Friday, were bowled out for 161 in the 50th over after electing to bat.
Tanmay Mishra, who had slammed 43 in the opening match, top-scored again for the visitors. The 19-year-old struck 33 off 51 deliveries with three fours before he was run out.
Hitesh Modi and David Obuya chipped in with 30 apiece.
Bangladesh's left-arm seamer Syed Rasel returned the best figures of 3-28 while left-arm spinner Abdur Razzak and paceman Mashrafe Mortaza bagged two wickets each.
The remaining matches will be held in Fatullah on Thursday and Saturday.