Maryland trailed by six with just under four minutes left, but Dez Wells scored four straight and a dunk by Jake Layman tied it at 63-63 with 1:49 to play.
After an empty trip for each team, Bojanovsky hit two from the line with 36 seconds remaining to put the Seminoles ahead and Wells countered with a pair at the other end with 15.1 seconds left.
Florida State worked the clock down and Ian Miller fired a pass inside to Okaro White, who was immediately double-teamed and fed Bojanovsky for the winning slam with 4/10ths of a second remaining.
Bojanovsky finished with 12 points and 12 rebounds for the Seminoles (19-12), who enhanced their NCAA Tournament hopes and advanced to a quarterfinal matchup with top-seeded Virginia on Friday.
Miller scored 17 points and Aaron Thomas added 14 for Florida State, which had won three straight before ending the regular season with a home loss to Syracuse.
Wells and Seth Allen each scored 18 points for Maryland, which was a founding member of the ACC in 1953. The Terrapins (17-15), who are heading to the Big Ten next season, were coming off an emotional overtime win over Virginia in their regular-season finale on Sunday.
Florida State scored the first four points of the game and opened a 17-10 edge midway through the first half before Maryland battled back and took its first lead at 21-20 on a pair of free throws by Nick Faust with 6 1/2 minutes to play. Another Faust free throw gave the Terrapins a 34-28 advantage, but the Seminoles scored the final four points to pull within two at the break.
Maryland led by as many as five early in the second half and held a 43-42 edge with 14 1/2 minutes remaining, but went cold while Florida State ripped off 11 straight points.
Thomas fueled the run with a dunk and three on consecutive possessions, as the Seminoles grabbed a 53-43 lead with 10 1/2 minutes to play. Wells hit two from the line to stop Maryland's drought, but Miller followed with a three to extend the Florida State cushion to a game-high 11.