Burgess delivered the winning points on a clever inbounds play and Jamie Skeen then blocked a Florida State attempt at a game-winning shot to advance the Rams' stunning run through the tournament.
On the day the NCAA field was announced, Virginia Commonwealth was widely criticized as being unworthy of an at-large bid from the Colonial Athletic Association. Now the Rams are one win away from the Final Four and will try to pull off what would be a shocking victory over No. 1 seed Kansas in the Southwest Region finals Sunday.
USC, Georgetown, Purdue and Florida State have fallen victims to the Rams, who led by as many as eight points in the second half against the Seminoles.
Florida State's Chris Singleton scored the final points of regulation on a shot from beyond the arc to tie it at 65-65. Singleton then scored on a dunk with 37 seconds left in the extra period to give the Seminoles a one-point lead.
Joey Rodriguez tried to put the Rams in front with 8 seconds to go but his layup attempt was blocked out of bounds. On the ensuing inbounds pass, Burgess slipped inside the Florida State defense, took a pass from Rodriguez and scored on a layup.
Florida State's Derwin Kitchen quickly brought the ball up the court and it appeared he had a chance at a layup, but he passed the ball out to Singleton. His shot was blocked by Skeen at the buzzer.
Burgess led the Rams (27-11) with 26 points.
Derwin Kitchen had 23 for Florida State (23-11).