It will be American's seventh championship game in school history.
Pee Wee Gardner added 15 points for American (17-15), which had five players in double figures and shot 61.9 percent from the field.
Schoof hit his first four 3-pointers of the game, the last for a 48-28 lead, to help the Eagles hit seven of their first 10.
American led by as many as 22 in the second half, but Colgate pulled within nine, 62-53, with 1:45 left on a Matt McMullen 3-pointer. American made 11 of 14 free throws the rest of the way.
Luke Roh had 13 points and 14 rebounds for Colgate (16-17).