The Seminoles (11-1) outscored the Buccaneers 46-16 in the paint behind the dominant play of the 7-foot-1 Alabi and 6-11 fellow freshman Xavier Gibson, who finished with a career-high 11 points.
Jamarco Warren led Charleston Southern (5-5) with a game-high 21 points, but the Buccaneers managed just seven second-half field goals.
On the heels of its most lopsided victory of the season, Florida State has equaled its best 12-game start in program history heading into Sunday's home game against No. 3 Pittsburgh.
Florida State led 36-26 at halftime and quickly extended its lead by attacking the basket. The Seminoles opened the second half with a 11-3 run to seize control.