The Panthers (5-8, 1-2 Big South Conference) made 11 of 16 3-pointers, with Barbour hitting 4 of 7 and Shine 4 of 5. Barbour also made 10 of 11 free throws.
High Point used a 19-0 run spanning both halves to turn a three-point advantage into a 46-24 lead with 18:30 remaining.
Charleston Southern (9-5, 3-1) chipped away, whittling the deficit down to six points, at 80-74, on Sheldon Strickland's layup with 42 seconds left.
After Barbour hit two free throws, Jeremy Sexton's 3 got the Buccaneers within five with 34 seconds left.
The Panthers made 6 of 6 free throws and Charleston Southern missed three 3-point attempts down the stretch.
Saah Nimley led the Buccaneers with 18 points and Sexton added 17.
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