Reed and Roberts combined to go a perfect 9 of 9 from the free-throw line. Eric Ferguson added 11 points for Georgia Southern (8-10, 2-3), which made just 6 of 24 shots in the first half and trailed 20-13 at intermission.
Georgia Southern never trailed by more than four in the second half and took a one-point lead four times before Ferguson's dunk put the Eagles up for good 45-44 with 42 seconds remaining. Reed sank two free throws and Roberts added four in the final 30 seconds.
Andrew Lawrence scored 15 for College of Charleston (12-6, 4-2), which was held to just one field goal over the final 3 minutes.
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