Butler (8-0) jumped out to a 36-21 lead, thanks in part to five 3-pointers from Hayward. The Bulldogs shot 59 percent from the field, including 8-for-16 from 3-point range, in the first half and led 44-31 at the break.
Bradley (4-4) pulled to within 62-57 with 8:27 left, but Butler put the game out of reach with an 11-0 run. The Bulldogs were 13-for-27 from 3-point range for the game.
Willie Veasely finished with 13 points for Butler.
Eddren McCain led Bradley with a career-high 18 points. Sam Maniscalco added 17 points and Theron Wilson added 15 points for the Braves.