Namibia won the toss and put Kenya in, Duncan Allen falling early on. Alex Obanda and Irfan Karim then put on 80 for the second wicket to take the score to 99, when Karim was second out having scored 23.
Obanda stayed in to reach 71 form 67 balls, and he had given his team a good platform, with the score on 113-3 in the twentieth over. But the Kenyans were unable to capitalise on that start, and were eventually bowled out for 187, Christi Viljoen taking 3-40.
Namibia's reply began with a 59 run opening partnership between Ian Opperman and Raymond van Schoor, which ended when van Schoor was trapped lbw for 32. Louis van der Westhuizen again failed and was out for a duck, but Opperman and Sarel Burger were able to put on 50 for the third wicket.
Opperman was eventually out for 45, but Namibia didn't lose another wicket, Burger and Craig Williams taking them home with a 78 run partnership to secure the seven wicket win, Williams top scoring with an unbeaten 59.
The win lifts Namibia of the foot of the World Cricket League Championship table to seventh, just behind Kenya in sixth place.
Namibia will next be in action in the Cricket South Africa inter-provincial competition, taking on Easterns in a three-day match starting on Thursday and a one-day match on Sunday. Kenya have no scheduled fixtures until the visit of Canada for Intercontinental Cup and World Cricket League Championship matches in 5-6 months time.