Winthrop (18-11, 12-6) came into the regular-season finale a game back of UNC Asheville, where the Eagles lost on Thursday, but fell behind by 19 points with nine minutes remaining. The Buccaneers made 10 of 12 free throws in the final 41 seconds to hold off the Eagles.
Xavier Cooks caught an inbounds pass at the center of the 3-point arc with 1.2 seconds left but his turnaround 3-point try missed.
Keeling became the fifth Big South sophomore to reach 1,000 career points. Cortez Mitchell added 10.
Charleston Southern (14-15, 9-9) had not won in Winthrop Coliseum since Jan. 24, 2002, a string of 16 losses.
Mannion, who recently reclassified and is ESPN's No.11 overall player in the class of 2019, chose Arizona over Marquette.
He'll fit in with Sean Miller's plans for a faster tempo on offense.
The cream of the crop of American high school basketball will congregate in Colorado Springs from Oct. 5-7, as USA Basketball unveils its newly expanded Junior National Team minicamp in collaboration with the NBA, NCAA and NBPA.