Tillotson finished with 6-of-10 shooting from the field and sank all four of his free throws for the Raiders (2-3). Alex Ramon scored 14 points and grabbed seven rebounds. Jordan Robertson added 13 points and Sean O'Brien had 11. The team averaged 45.8 percent shooting from the field and 77.3 percent from the line.
Robertson and O'Brien combined for four 3-pointers in the final seven minutes of the first half to help Colgate to a 37-24 advantage at the break.
UMBC battled back to close the gap to six on a 14-9 run late in the second half to trail 62-56 with 1:55 to play but a Tillotson steal and ensuing bucket helped keep the Raiders in the lead during the final minute.
Will Darley led the Retrievers (1-6) with 18 points.