Appalachian State made seven 3-pointers in the first half to take a 44-29 lead into halftime.
Presbyterian (2-10) rallied in the second half. Trailing 50-34 with 17:03 left to play, the Blue Hose went on a 21-13 run to get within eight, 63-55, with 7:47 left to play.
Appalachian State responded with an 8-2 run to push the lead to 14, 71-57 with just under three minutes to play.
Jordan Downing made two 3-pointers to help Presbyterian cut the lead to four, 74-70, with 28 seconds left, but Baskin connected on four straight free throws to seal the win.
Downing led Presbyterian with 21 points and five rebounds.
Kory Holden, the No. 2 available transfer in ESPN's rankings after averaging 17.7 points last season for Delaware, is transferring to South Carolina.
College basketball has a problem as players continue to transfer schools at an alarming rate. Fleeing a program for more playing time isn't always the best solution.
The Florida Gators have added ESPN top-10 prospect Gorjok Gak to their 2016 recruiting class.