Radford was up 70-59 with 4:49 left, but Presbyterian stormed back to trail by just one with 27 seconds left. Radford's Rashun Davis made two free throws with 20 seconds remaining and Presbyterian's Jordan Downing missed a long 3-pointer that would have tied it. Javonte Green sealed it with two free throws.
Green finished with 16 points for Radford (21-11) and R.J. Price added 15.
Downing scored 32 for Presbyterian (6-26) and Reggie Dillard had 13.
After surrendering a 19-4 run, Presbyterian got within single-digits until Davis' 3-pointer, Radford's seventh of the game, ended an 8-3 PC run and gave the Highlanders a 65-54 lead with 7:12 left.
Radford will play No. 2 seed UNC Asheville in the quarterfinals on Friday.