The Falcons (15-5, 6-3 PBC) trailed by as many as 18 points in the first half at 41-23 and were down 41-28 at the break before outscoring the Jaguars 46-25 over the final 20 minutes.
Montevallo took the lead for good at 56-55 on a 3-pointer by Travis DeShazior with 6:07 to play. Ryan May led the Falcons with 18 points.
Devon Wright-Nelson scored 13 points to lead Augusta State (12-8, 8-4). O'Neal Armstrong and Devonte Thomas added 10 each.
In the women's game, Augusta State picked up a key road win, 64-59.
Jeminah Ashby scored 14 points to lead the Lady Jags (10-10, 5-7 PBC). Amber Peterson added 11 and Eryka Menzies had 10.
With the victory, the Lady Jags reached the double-figure mark in wins for the first time since the 2007-08 season.
Taylor Beverly scored a game-high 16 points for Montevallo (7-11, 2-7).