The Antelopes (18-2, 5-0 Western Athletic Conference) used a 12-0 run to lead 65-51 and made all eight free throws in the final minute to hold off a late rally from UMKC.
Braun was 6 of 9 from 3-point range and scored 18 during the second half. Braun topped 30 points for the second time in three games after setting a career high of 34 in a 99-88 win over Utah Valley last Saturday.
The Antelopes were 10 of 17 from 3-point range with Ryan Majerle making all three of his long-range attempts for nine points.
UMKC closed within five with 47 seconds to go.