Rafique scored a brisk 33 and then grabbed 5-47 on Thursday as the home side clinched the series with a match still remaining.
Electing to bat first, Bangladesh scored 231, which proved enough to continue their winning streak after having already taken an unbeatable 2-0 lead. Kenya were bowled out for 211 in reply.
Opener Shahriar Nafees and middle-order batsman Alok Kapali slammed fine half-centuries to boost the home side.
Left-hander Nafees, who scored 91 in the opening match, continued his fine form to strike a determined 57 with 10 fours while Kapali returned to form with a well-paced 55 to help recover from 132-6.
Seamers Peter Ongondo and Steve Tikolo bagged three wickets each but with former captain Khaled Mashud (39) and Rafique on form, Bangladesh were never in much trouble.
In reply, Kenya were rattled by an early twin-strike from paceman Mashrafe Mortaza, who dismissed openers Kennedy Otieno (1) and David Obuyo (13) before Rafique came on to torment the batsmen.
Tanmesh Mishra (48), Collins Obuya (45) and Hitesh Modi (37) did well for Kenya, with Mishra continuing his fine form after scores of 33 and 43 in the previous two matches.
Bangladesh won the first match by 131 runs in Bogra and the second by nine wickets in Khulna.
The final match will be played here on Saturday.