Reza, who ended the match with an unbeaten 34 proved the perfect foil for the experienced right-hander Ashraful as they steadied the Bangladesh innings after a shaky start on Saturday.
Ashraful played a pivotal role in the match-winning partnership with 12 fours and one six from only 60 deliveries which ensured the the tourists wrapped up the match by almost 20 overs to spare.
But it was paceman Mashrafe Mortaza who did the damage when he claimed 3-25 as the hosts were dismissed for a paltry 168 after being send in to bat.
The 22-year-old further exposed the weak Kenyan top order when he took three quick wickets in his opening spell and spinner Abdul Razzak added three more.
Razzak accounted for the priced wicket of Steve Tikolo who top-scored for his side with 47.
The second of the three one day internationals is on Sunday in Nairobi.