Wesleyan had 10 fewer turnovers, did an adequate job of rebounding and had balance in scoring with four players in double figures, but shot just over 30 percent from the floor in regulation before canning five of eight shots (62 percent) to pull out the victory.
Amy Jo Castor, Ashton Burrell, Gibson, Jackson and Katie Blevins all hit 3-point goals in the first half, but the Lady Bulldogs saw an 18-9 lead shrink to a single bucket at 28-26 by the intermission.
Wesleyan's shooting woes continued into the second half as Brevard forged in front 47-37 with 14:06 to play. Blevins had a '3' among six points and Jackson's trey with 10:06 remaining knotted the score at 51. Another dry spell, however, allowed Brevard to open an eight-point gap at the 4:11 mark.
The Lady Bulldogs held he visitors to just two free throws from there while Ragan Elliott and Candance Cain connected from the free throw line and Jackson nailed a three-pointer to set up Gibson's dramatic bucket at the buzzer.
Trailing 72-70, Elliott converted an offensive rebound into a three-point play and followed a Brevard turnover with a layup, boosting the margin to three.
Jackson's final three-pointer and free throw in the closing seconds preserved the victory.
Jackson netted 21 points, Castor 13, Blevins 12 and Elliott 11 to go with a team-high 11 rebounds.