USC Upstate (19-13) led 38-30 at half and maintained a double-digit lead for most of the second half before holding off North Florida (16-16) late.
The Ospreys cut the lead to 68-62 with 4:10 remaining, before Glenn responded with a three-point play. The lead was cut to 75-70 with 37 seconds left, but USC Upstate hit 5 of 6 from the line in the last 35 seconds to preserve the win.
Glenn also had nine rebounds. Ty Greene scored 14 while Fred Miller had 13 and Jodd Maxey 12.
Chris Davenport had 27 points and 10 rebounds to lead North Florida. Dallas Moore added 13 points and Travis Wallace had 12.
USC Upstate advances to play second-seeded Mercer on Thursday in the tournament semifinal.