The Shockers (30-0, 17-0 MVC) shot 48.9 percent from the field and moved to within one win of an unbeaten regular season.
Baker made 6-of-12 shots from the field and had six rebounds. He was one of four Wichita State starters in double figures.
Wichita State led 35-25 at halftime and benefited from a woeful 27.1 percent shooting percentage by the Braves (12-18, 7-10), who have lost four of their last five contests.
Walt Lemon led Bradley with 18 points. Tyshon Pickett scored 13 points and 15 rebounds.