The 21st-ranked Bears led by only four at halftime and Charleston Southern climbed to within three inside the final minute on a 3-pointer by Will Saunders.
Saah Nimley had a chance to tie the game with 11 seconds left, but his 3-pointer bounced off the rim and Chery's free throws clinched Baylor's fourth win in as many games. The Buccaneers fell to 2-3.
Cory Jefferson and Isaiah Austin had 16 points each for the Bears and Jefferson collected a dozen rebounds. Brady Heslip contributed 11 points off the bench.
Charleston Southern was led by Saunders with 16 points.