Jeremy Evans had 11 points and 10 rebounds for Western Kentucky.
The Hilltoppers (16-7, 8-3 Sun Belt) shot 55 percent from the field overall and 78 percent in the second half to hold off Denver (3-18, 2-9).
Tyler Bullock made a 3-pointer with 13:23 to go to pull Denver to within 40-37.
Brazelton responded with his own 3-pointer, then stole the ball from Bullock on the next possession and hit a layup to give Western Kentucky a 45-37 cushion.
The Pioneers pulled within five points with 8:12 left but got no closer.
Western Kentucky led by as much as 14 in the second half.
Bullock scored 20 points to lead Denver, and freshman forward Nate Rohnert had a career-high 17 points.