Xavier Gibson also had 13 points for the winners while Georgetown's Eddie Gray led all scorers with 19 points.
Florida State, which led 33-28 at halftime, opens its regular season at home next Monday against Jacksonville University.
The Seminoles, who finished 25-10 last year and were the runner-up at the Atlantic Coast Conference tournament, are coming off their best season since 1992-93 and their first NCAA tournament invitation in a decade.
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