Regisford made 6-of-8 field goals and 8-of-10 free throws and Rivard was 7 of 8 from the field for the Raiders (10-9, 6-2 Patriot), who went 7 of 15 behind the arc and shot 54 percent overall. Sean O'Brien hit three 3s and scored 15 points and Austin Tillotson added 10.
Jordan Swopshire hit a 3-pointer at the buzzer to give Colgate a 33-29 lead at the half.
O'Brien hit a 3 to cap a 7-0 spurt that put the Raiders up 68-54 with 5:39 to play. Robert Champion's jumper pulled the Crusaders within 10 with 3:45 left but they didn't make another field goal until the closing seconds.
Colgate scored its final eight points from the line and went 19 of 23 overall.
Anthony Thompson had 14 points for Holy Cross (8-11, 3-5).