High Point (13-17) will advance to face No. 1 seed UNC Asheville on Wednesday night on the Bulldogs' home court.
Gardner-Webb (12-20) got a team-high 21 points from redshirt junior Tashan Newsome, but could not find its range from outside - shooting just 5-32 from 3-point range for the game (15.6 percent).
With the Runnin' Bulldogs cold from deep, the Panthers remained packed in a zone defense for much of the game, and made enough shots themselves to keep the lead down the stretch.
Nick Barbour led High Point with 22 points, Corey Law added 16 points and 11 rebounds and Shay Shine knocked in 11 points to lead the No. 8 seed Panthers.
The Runnin' Bulldogs made just 1-of-17 (5.8 percent) of their 3-point attempts in the opening half and trailed 28-22 at the break.
Gardner-Webb tied the game at 29-29 early in the second half, but High Point responded with a quick surge to go up by nine with 10:50 to play. GWU would not get the margin down to five points several times in the final 10 minutes - doing so as late as 2:19 left on a Tyler Strange 3-pointer to cut the lead to 53-48 - but the Panthers were able to answer each time.
After Strange's trey, Barbour knocked down two free throws to push the lead to seven, Law converted a dunk after a turnover to push the lead back to nine and Barbour made the score 59-48 on a put back with 1:31 left in the game - and made another free throw with 1:23 left for a 60-48 score.
Newsome started a quick spurt by the 'Dogs moments later, knocking down a long jumper and stealing the inbounds pass before dishing an assist to David Brown for a 3-pointer and a 60-53 score with 1:03 left.
Gardner-Webb was forced to foul down the stretch and could not get any closer as the Panthers knocked down their free throws to seal the game.
The Runnin' Bulldogs shot 34.3 percent for the game (23-67), staying in contention with a workmanlike effort on the offensive glass (22 offensive rebounds). Newsome was the only other player in double digits for Gardner-Webb. Laron Buggs scored eight points in his final game with the 'Dogs, and Brown netted six in his final appearance.
High Point shot 40.7 percent for the game (22-54), made 18-of-27 free throws (66.7 percent) and stayed even on the glass (42-42) with Gardner-Webb. Jairus Simms and Branimir Mikulic each had eight points for the Panthers.