Keaton Cole had 16, Tawaski King 14, Trey Sumler 12 and Brandon Boggs and Preston Ross had 11 apiece for the third-seeded Catamounts (16-17).
Wofford (19-13) entered intermission trailing 38-32 but Western Carolina opened the second half on a 13-4 run to take a 51-36 lead with 15:36 left to play.
The Catamounts pushed that lead to 77-59 behind a 3-pointer from Cole with 3:16 remaining.
Western Carolina outscored second-seeded Wofford 44-27 in the second half and held the Terriers to just 32.8-percent (20 of 61) shooting overall. The Terriers hit just 3 of 24 3-point attempts.
Brad Loesing led Wofford with 23 points but shot just 8 of 17 from the field.
Western Carolina takes on UNC Greenville on Sunday in the semifinals.
- Western Carolina overpowers Wofford 82-59
- Tar Heels ready for Final Four push after title-game loss
- Freshman class makes Duke a title favorite once again
- Police: South Carolina guard Felder kicked officers
- Clemson looking to end NCAA Tournament drought this season
- Defending champion Oregon picked to repeat as Pac-12 winner