Jamaal Trice added 12 points and Mike Neal chipped in with 10 for the Mountaineers (3-8).
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.
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