After the Ospreys pulled ahead 75-74 on an Andy Diaz layup with 29 seconds left, Gollon hit a jumper, blocked a shot and made two free throws with 4 seconds to go.
Parker Smith's potential tying 3-pointer rattled around the rim without falling with 1 second left, giving the Bears (13-15, 10-7 Atlantic Sun Conference) their fifth straight win and a split of the season series.
North Florida (10-18, 7-10), which beat Mercer 74-64 on Jan. 22, has lost four of five.
Mills, who scored 22 second-half points, made 11 of 22 field goals while his teammates were a combined 14 of 43. Three Bears fouled out in the last 5:41.
Brad Haugabrook scored 19 points and Jimmy Williams had 18 to pace the Ospreys.