Schoof, who entered a 50-percent 3-point shooter on the season, hit 5 of 8 from deep and has at least one 3-pointer in seven consecutive games for the Eagles (9-14, 4-4 Patriot League).
Colgate took a 26-25 lead shortly after halftime and was tied 36-36 with 13 minutes left.
Wroblicky snapped that tie with a jumper, which sparked a 16-2 Eagles run that included two 3-pointers and a layup from Schoof.
Florida State's student government has passed a resolution discouraging Seminoles fans from wearing Native American headdresses at games.
The second annual Gavitt Tipoff Games, eight games between members of the Big East and Big Ten to be played Nov. 14-18, will feature Villanova at Purdue in the opener.
Michael Lewis is leaving his assistant coaching job at Butler to take the same position at Nebraska under Tim Miles.