With the win, the Crusaders (15-13, 10-3) will be no worse than second seed in the Patriot League Tournament.
The score was tied at 11-11 after the first seven minutes, but the Crusaders went on a 15-4 run over the next seven minutes to take an 11-point advantage, 26-15. The Raiders scored the next eight points and then tied the score at 28-28 at the half.
Colgate started the second half with a 12-3 run to go up 40-31 before Holy Cross responded with a 17-5 spurt and took the lead for good.
Both teams end their regular seasons Saturday: Colgate at Navy, Holy Cross at home against Lehigh.