The Red Raiders (7-11, 4-1 Patriot League) had not beaten the Terriers (7-9, 3-2) since 1976. BU had won eight-straight league games dating back to last year.
Colgate was trailing by three when Pat Moore hit a 3-pointer with 7:14 left to start a 12-2 run. Damon Sherman-Newsome and Matt McMullen also knocked down 3s and the Red Raiders led 56-47 with 1:27 left when Luke Roh made his second basket of the run.
After Cedric Hankerson made a 3 with 1:18 to go to pull BU within 56-50, Colgate made 6 of 8 free throws.
Roh added 13 points for Colgate, which shot 55 percent in the second half.
Eric Fanning led the Terriers, who led 29-26 at halftime, with 15.