The Terriers (26-8) captured their first title and gained the automatic bid to the upcoming NCAA Tournament.
Noah Dahlman had 10 points while Tim Johnson grabbed 13 rebounds for Wofford, which defeated UNC Greensboro and Western Carolina to reach the title game.
Trailing by 18 points early in the second half, the Mountaineers clawed their way back into the game with 10 straight points. Williamson capped the run on a pair of buckets, with the last coming with just under 13 minutes to play to make it a 36-28 game.
Wofford continued to lead by two or three possessions for the next several minutes, but Abraham was fouled as he buried three-pointer and he hit the free throw to make it a four-point game, 48-44 with 2 1/2 minutes to play.
Rundles followed with a free throw, and both sides missed several attempts at either end.
Williamson put in a free throw with just under a minute to play to again make it a four-point game, but Terry Martin followed with two from the line for Wofford.
After Abraham quickly sank a layup, Rundles was fouled and drained his two attempts.
A Williamson slam was countered by 1-of-2 from Brad Loesing, but Rundles stole the ball from Abraham and hit a free throw to make it a six-point game with 19 seconds left to essentially seal the win.
The Terriers scored 17 of the first 20 points in the game, and maintained a significant lead through the remainder of the first half. A Rundles free throw followed by a Jamar Diggs jumper closed out the scoring in the half to give Wofford a 33-18 lead after 20 minutes.
Appalachian State leads the series, 22-11...Wofford shot 35.2 percent in the game while Appalachian State hit 28.8 percent of its shots.