The Seminoles (18-5, 6-2 Atlantic Coast Conference), coming off a 9-point home loss against No. 13 North Carolina, led 39-32 at halftime and used a 14-4 burst to open the second half to seemingly take command until Virginia made a frenetic push to make it close.
Virginia (13-12, 2-7) used a 21-7 run to close to within 74-72 on Ariana Moorer's layup with 47 seconds left, then stole the inbounds pass, but Paulish Kellam was called for traveling while driving to the basket and Natasha Howard scored at the other end.
After another basket by Virginia's Ataira Frankling with 5 seconds left against made it a 2-point game, Bravard hit a pair of free throws with 3.9 seconds to play to clinch it.
Franklin led Virginia with 16 points and China Crosby had 14.
Alexa Deluzio added 15 points and Courtney Ward had 13 for the Seminoles.
Leading 67-51 with 7:23 to play, Florida State seemed well on its way to an easy victory until its shots stopped falling and the Cavaliers suddenly started making everything.
A drive by Franklin, two free throws by Whitny Edwards and four more by Crosby pulled Virginia to 69-62. Bravard hit two free throws, Crosby scored on a drive and Bravard scored inside before Edwards' 3-pointer for Virginia pulled them to within 73-67 with 1:47 left.
Olivia Bresnahan made a free throw for the Seminoles, and Franklin hit a 3-pointer from the right corner with 1:33 to play, making it a four-point game. After the Seminoles missed, Moorer scored on a drive with the shot clock running down, her only field goal of the game.
That set up the wild finish, which sent Virginia to its third loss in four game. The Cavaliers look increasingly like a team that will need a huge surge the rest of the way or in the ACC tournament to avoid hosting NCAA tournament games without being in the field.
Florida State dominated inside, outscoring Virginia 40-22 in the paint.