David Collins, with 10 points and 10 rebounds, was the only player in double figures for Bradley (16-13, 9-8).
Evansville led 30-20 at the break and never trailed. The Braves got no closer than three after the break.
The Purple Aces shot 40 percent from the field and 3-of-9 from behind the arc. The Braves shot 34 percent from the field and 6-of-24 from 3-point range. Both teams made about 63 percent of their free throws.