The Terriers (2-4) trailed 25-12 at the 2:14 mark, then closed out the first half of the Nations of Coaches Classic game with a 7-2 run.
Skinner made two layups to open the second half, and his 3-pointer with 5:19 to play tied it at 40.
The Pirates (0-4) rebuilt a three-point advantage, but Karl Cochran scored seven straight points to finish with 18. Skinner added a layup to give Wofford a 49-43 lead with 53 seconds left. The Terriers sealed the win by hitting 7 of 8 free throws.
Wofford shot only 32.1 percent from the field (18 of 56), but had 14 steals and forced 24 turnovers.
David Bruce led Hampton with 10 points and 12 rebounds.