The Mountaineers (13-17), seeded fifth in the league's North Division, shot 62.5 percent (20 of 32) in the second half, when Neal scored 16 of his points and Carter 13.
Appalachian State led 33-30 at the half, but Charleston (19-12), the South Division's fourth seed, tied it at 42 with 14:27 remaining. A 15-5 run, ending with a three-point play by Neal, gave the Mountaineers a 10-point lead, 57-47, and it was 63-51 with 8:37 left after two 3-pointers by Carter.
Tab Hamilton had 17 points, Isaac Butts 11 and Andre Williamson 10 points with 15 rebounds for Appalachian State, which plays UNC Greensboro in the quarterfinals Saturday.
Trent Wiedeman led Charleston with 19 points, and Antwaine Wiggins and Andrew Lawrence scored 14 each.
- College of Charleston