It was the largest road conference victory by the Braves in 10 years.
Darrell Brown had 16 points for Bradley (11-5, 2-1 Missouri Valley Conference). Ja'Shon Henry added 14 points and nine rebounds, and Koch Bar had nine rebounds.
Evansville put up 19 first-half points, a season low for the team.
Bradley plays Southern Illinois at home on Saturday. Evansville takes on Loyola of Chicago on the road on Saturday.