Medium-pacer Mashrafe Mortaza acted as the chief destroyer of the Kenyan batting line-up taking 6-26 here on Tuesday for his total haul of 13 wickets in the three-match series.
Fellow pacer Syed Rasel had negotiated the early collapse when he trapped the out-of-form opener Kennedy Obuya for a duck with the first ball and Morris Ouma was the next to go when he was clean bowled by Mohammad Rafique.
The only Kenyan player to put some resistance was Thomas Odoyo (29) but he could not repeat the same performance of the second match. Odoyo became Mortaza's fourth victim to fall in his opening seven-over spell.
In reply, openers Shariar Nafees and Mohammed Ashraful scored quick runs for Bangladesh to close the gap before the lunch but after their departure soon after the break meant the match would last longer than expected.
The visitors also endured some anxious moments when two of their batsmen Tushar Imran and Saqibul Hasan were both run in the 17th over. It was Imran who was given out.
In the end the onus of clinching victory fell on the young shoulders of Saqibul Hasan and Farhad Reza, whose fifth-wicket partnership stand of 53 took Bangladesh to victory in the 27th over.