Ball State raced out to a 17-6 lead 6 1/2 minutes in thanks for 3-pointers by Francis Kiapway and Zavier Turner and led 38-30 at the break.
Miami (8-13, 3-5 Mid-American) clawed its way back to tie and take the lead on a pair of free throws by Will Sullivan with 8:38 left.
After a few taut minutes, Zach McCormick's 3-pointer with 2:13 left put Miami up 69-68. Matt Kamieniecki responded with a layup to re-take the lead briefly. But Miami reeled off the next seven points and made 5 of 6 free throws down the stretch to seal it.
Will Sullivan had 13 points for the Redhawks, Logan McLane added 11 and Geovonie McKnight chipped in 10. Miami shot 56.5 percent.
Ball State (7-12, 2-6 Mid-American) was paced by 15 points apiece from Franko House and Sean Sellers.