Florida State took its only lead of the second half at 55-54 on Jason Rich's layup with 3:45 left before Duke put the game away with a closing 16-2 run. Kyle Singler's 3-pointer put the Blue Devils ahead for good with 3:30 to play.
Duke (14-1, 2-0 Atlantic Coast Conference) nearly blew a 17-point lead it built in the first half on a 16-0 run led by Scheyer, who had 10 points on a variety of shots in a span of just 1:35.
The Blue Devils led at halftime, 34-22, before Rich, who had all 18 of his points in the second half, keyed the comeback by Florida State (12-6, 1-2).
Toney Douglas added 13 points for Florida State, while Uche Echefu, who had 24 points and 12 rebounds in a double-overtime loss at Clemson on Saturday, was held to six points and seven rebounds.
Gerald Henderson added 11 points, and Singler had 10 for Duke. Henderson's eight rebounds helped the Blue Devils to a 44-32 advantage on the boards.
Duke managed to get the road win despite shooting 43.9 percent and committing 20 turnovers. Florida State shot 35.5 percent.