Tony Wroblicky added 14 points and 10 rebounds, and contributed a pair of late dunks to ensure the second-seeded Eagles (18-12) will host third-seeded Holy Cross in a semifinal Saturday.
Darius Gardner added 12 points for American, who won at seventh seed Colgate on Jan. 11 before losing at home to the Raiders (13-18) four weeks later.
Murphy Burnatowski scored 15 points for Colgate, which saw its win streak snapped at four in a season-ending defeat.
Austin Tillotson and Damon Sherman-Newsome each added 10 points as the Raiders failed to come back after American assembled an 18-0 first-half run to lead by as many as 17.
American shot 70 percent (14 of 20) from the foul line. Colgate shot just 50 percent (9 of 18) while tying season-lows for points in a game and in a first half.
Down 30-15 at halftime, the Raiders gradually cut into the lead, first drawing within 11 four times before Burnatowski's baseline 3-pointer closed it to 42-32.
Sherman-Newsome later cut the deficit to nine with a foul shot and eight with a 3-pointer before Ethan Jacobs' inside basket made it 50-43 with 1:54 left.
Wroblicky answered with a transition dunk off Schoof's long feed. After Burnatowski's free throw again closed it to seven, Wroblicky slammed in another to make it 55-46 with 1:00 left.
Schoof hit a pair of 3-pointers during an 18-0 run that gave American a 24-7 lead, before Burnatowski's jumper finally ended a 10:57 stretch without a Colgate field goal.
The Raiders missed 12 field goal attempts and committed five of their seven first-half turnovers in that stretch.